What do I have to do to buy this house in Riften? I've done the skooma quest for the Jarl and about two other miscellaneous quests.

You need to do more quests before the Jarl will trust you. Keep doing favor, miscellaneous, and side quests for the townsfolk and check in each time with her steward. The option should pop up eventually.

There are a crapton of misc. quests to do in Riften. http://www.uesp.net/wiki/Skyrim:Riften

Take your pick.

You need to do 5 quests for the citizens of riften.

I did a Temple of Mara quest, the skooma quest and a think a delivery quest and then I got made Thane and got the house. Got it yesterday actually its a really sweet house I really like it.