Personally I really like puzzle and rpg porn games since I like to play one handed. *Wink wink nudge nudge poke poke* And match 3s tend to be my go to, Huniepop did a great job with it, too bad the writing in the sequel went... weird. There was a tetris attack game called Octofurry that was pretty good.
I'm not used to thinking of Mahjongg as social (just played mahjongg solitaire) but that could be really cool, you with a few characters playing together, especially if they had fun with each other, but probably a lot of work. Especially if you did animations with similar quality to Monster Mind and both gender options.