I have seen this post over the years (since it was posted) and have always thought of replying so now finally doing so. (This will be a detailed post and would cover most of what I have learned by surveying and university projects and even direct interviews with some of the companies).
In the original post, the OP presented a few options. Let me tell you this, nearly ALL of the good brand have good quality (those that have decided to name themselves and establish themselves as a brands). Do not get into the gimmick done by these so-called "International" companies offering superior quality and whatnot.
ICI (which is now called AkzoNobel since ICI Pakistan is another company altogether and does not make paint), Nippon, Kansai (the japanese paints are here because of Honda, Toyota and Suzuki as they only buy auto paint from them for their cars) and Jotun are the only international paint company we have in Pakistan (I may missed some of them) and all of them are "made" locally at their plant in Pakistan. So any price (premium) they charge is just them making more bucks for giving the same quality as their local Pakistani brands (now I have mentioned brands here not local chona wala paints those are considered as unbranded paints).
Berger is a special case here, it is a Pakistani brand and has nothing to with Berger International. Berger was a UK based brand years ago but in the early 90s the English men sold the company to Indian investors (and as you know it keeping the company in Pakistan was difficult for the new Indian owners so they sold the business to their Pakistani distributor who then registered the company in Britsih Virgin Island under a what people might call as a "Panama leaks" company called Slotrapid U.K.) so now the owners are Pakistani and the brand BERGER Paints Pakistan limited is Pakistani and anything else they portray is just 'claiming' their past heritage. (you can check Panama leak list of companies you can find Slotrapids in the list and also check any of Berger paints annual report available at their website you can see that Slotrapid has more than 50% ownership of the company).
Now moving on to local paint companies....
Most of all the paint makers are having about 3 to 4 "Brands" which serves as their "qualities" and are available at different prices, ranging from premium to absolute trash. You as the buyer need to sort out which one is for you (mind you even the so called International players are doing this). Its not that the trash quality is very bad but people buy them thinking they have gotten the best paint while in reality they have gotten a very lower end ones.
Now I am going through the names (one by one as per the original post) and will add other companies names too.
Nelson is one of the major players in Karachi. It has currently at the time of writing this post: NELSON, BOLD, BRITISH, SPLENDOR and God knows how many 'qualities'. So be careful with what you choose. They are one of the expensive sides in the local 'brands' (yes they invest in their name so they are a brand). I have always found their prices on the higher side among other similar quality paint but be sure to not fall for the BOLD, BRITISH and other sub qualities they have (golden rule for them is if it been slightly cheaper then their main quality then it is the lower brand). (Established in 1995)
Kote (although I am unsure which brand you meant but I am assuming you mean SuperKote). SuperKote is a fairly new company and is predominantly in Karachi (mostly) and was established in 2015. They also have multiple 'qualities' so advise is caution. Price is moderate (better than Nelson's) and quality is dependant on whatever tier product you choose as they have multiple qualities all marketed under SUPERKOTE name (streamline,smart range,project pack etc). Just don't get these ranges and go only for the main SuperKote pack (without any sub brand series, it might not still be the best quality but it would be their best).
Rainbow is a Karachi based brand but it has accordingly to my research (might be the only Karachi based one) that has presence in most part of Pakistan. Their distribution network is not so great to be honest but products are good. To my knowledge they only make 1 quality (Rainbow) which is surprising since most other brands make multiple qualities. According to the market they are known for their Wall Putty and Water Base Matt (Interior) and are one of the oldest companies in Karachi (established 1981). The negative feedback about them is not because of any quality issues but that there products are almost short in the stores (so either they have exceedly high demand or quality or have a poor distribution network). I guess since they have only 1 quality (which they proudly claim that they only make premium quality I guess you can give them a try). Prices are not too bad if you compare it with other brand 'premium' ones.
Happilac is a Faisalabad based brand (and one of Faisalabad biggest and oldest too 1978-9). They made their money on the Afghanistan boom (during the post 2001 period when they exported to Afghanistan) and are now trying grip Pakistani market too (They have a good presence in central punjab region). Quality is okayish; not something spectacular but not bad too. (still the price is very high for the quality; I think taking Afridi as a brand ambassador might have its costs 
)
Now as the OP posted that paint is not covering (since I don't know the detail and can't judge), please note that our country's painters are extremely greedy people and there are very very few extremely honest ones (and even fewer that even know how to paint properly). They are used to the product to be in a certain way and if it isn't they throw a tantrum and destroy the paint. (and also they get commission from different companies to use their product too). Most likely the painter didn't get the Token they wanted in Happilac (meaning they might have given 100Rs and the painter wanted 150rs) and for this the painter purposely did what he did. (The painters in Karachi are skewed toward Gobis, Nelson and Reliance since they offer the highest Token money and schemes etc to them and like I said there is very little major difference in the quality besides the prices)
Moving on, Dulux also has many different qualities like Dulux Promise, Paintex Star, Pentalite. Now the main qualities of Akzonobel are good but they are almost 1.5 times to 2x the price of any other paint. Even Promise and Paintex are expensive (and these are 3rd tier brand of the company). So unless you really want to spend more and have brand conscious phobia that 'we painted using ICI' then this is the brand for you. (note it is made in Lahore using roughly the same raw material as other manufacturer use; they just have a higher profit margin). The only plus point of using Dulux is that painter would not be able to hoodwink you as the consumer because however poor the paint is he cannot bash an imported brand as old as Dulux.
(I did a test with my local painter in which I took 3 different paint brands of equal quality (now the price was vastly different) as a sample and asked the painter which one I should buy for my house. He blindly recommended me 1 brand he was skewed towards. He painted 3 small samples and then reported that BRAND(A) is best while BRAND(B) which was ICI is also good but expensive and BRAND(C) which was a local brand is not good (his exact words were "covering nahi de raha"). Now comes the good part, I provided him the same paints again but now I removed the labels and gave him unmarked cans, and as expected he was not able to distinguish much between them. He in the end identified his favourite one using the smell of perfume used by that company, The problem of 'covering' had miraculously disappeared).
Diamond has 4 qualities: ACE, OVERALL, VALUE and EVERLAST. Now any company that makes this many quality openly is weird. ACE is their prime quality (so would only recommend getting ACE and if you are on a budget OVERALL nothing below this please). Diamond is Lahore based (and was established in 1983). Again the ACE series is as much expensive as DULUX so there is that.
Now since the last post mentions Brighto:
Brighto is not a bad paint but I would NOT classify it as 'excellent'. It is very much expensive, the Stain Free is priced at Rs 3925 per gallon (at the time of writing this post) even Berger's Elegance Matt Emulsion isn't that much expensive (Rs 3317 per gallon) and mind you people actually like Berger in Pakistan blindly. So from a consumer point of view, it is not the best brand to go for. (I am guessing they are cashing-in on their PSL sponsorships by pricing so insanely high)
Again Brighto also has different qualities present: Wall Emulsion (2nd tier) vs Super Emulsion, All-Weather vs Wall Shield (2nd tier) and so on. From what I have noted that there distemper SUPER EMULSION isn't that great comparing to other local brands (same is the case for Weather as it is insanely high priced for providing the same quality)
Gobis is having different qualities too: Gobis Gold, Gobis Silver etc (it is established in 1981). Gold is absolutely their 2nd tier and is priced very high and they offer the most (you can call it bribe if you want since I don't know what to call it) to the painters -Blankets in winter, Rashan in Ramadan etc so that they use their brand over others (and as we know our painters are a greedy bunch). Quality is ok, but pricewise it isn't. (I would say avoid GOLD Series).
In the end I would also like to mention that almost all good paint provide a similar coverage (no difference other then pricing). Painters purposely overdilute or under-dilute the paint in order to destroy the paint so that they can convert you to whatever they want to use. Also please be sensible while selecting paints, like RED colour in exterior is fine but it demands using a quality weather resistant paint (and not interior based paints as they would fade too quickly or using 2nd/3rd tier qualities). Also surface preparation is a must (and so is using the appropriate primers, sanding, filling etc depending on the surface.
