First of all, I don't think it's the black color of the tar that makes the apartment so hot, there are so many buildings with tar on the roof and some of those apartments are not so hot. The reason for that is that there is good weather proof insulation between the tar and the apartment. I think your brother's problem is lack of proper insulation rather thenthe tar on the roof.
I don't know whether your bother owns or rent the apartment, and how much money he wants to spend on a solution. The proper expensive way of solving this would be to invest in really good insulation. It's expensive, but in the long run it will save a lot of money in heating \ AC bills.
A couple of cheap ways of cooling down a space without having to spend a lot of money - if the apartment in very sunny, it might be a good idea to get some shutters \ blinds to block some of the sun out, if the windows are shade, then it's also a good idea not to open all the windows all the time to let the heat in, but to open just 2 windows that are in different walls to let some air flow.
Another cheap but powerful trick - get a fan (doesn't even have to be a big expensive one, and hang a wet sheet in front of it - it might make the place look strange, but the wind from the fan will blow the water from the sheet into the apartment and cool it down.
Also - get a lot of potted plants and water them on a regular basis - it works in the same way walking through a parkk is often cooler then walking through a street.
Hope this helps.