I liked banafish's reply very much. I don't have specific repertoire to suggest, I just use whatever I think the students will enjoy and can (almost) play, unless they have requests. But you specified the hand coordination problem, and I do help a lot of people with that. It's a new physical challenge, but I don't think that's a big part of it, at least not in the way that it would seem. I think two other factors are much more significant: the psychological aspect, because most adult students tried to play as children and failed (at least, in their own judgment), and usually putting their hands together is what did them in at the time; and what I suspect is the biggest obstacle, the mental coordination, in which the brain needs to have made specific connections to correctly direct the nerve impulses. If the brain is unclear about how to direct all that traffic, it sends mixed signals and the hands seem very disobedient, although they are perfectly obeying the mixed-up orders they're receiving. Those neurons have to fire away and literally, physically make new connections between parts of the brain to do this new activity, and they don't get made because students read and play everything hands separately first. I have the students stop playing separately, just stop completely. This is difficult! Everything out in the world works against it, because it's "common knowledge" that we have to play everything HS first, and because if the student is only successful (in his mind) when playing HS, it's hard for him to give that up (understandably). At this point, I usually teach them BY ROTE something to play hands together. I don't need to do this with children unless they're unusually discouraged, but as you've noticed, the adults find the difficulties demoralizing, and you have to break the cycle and almost trick them into succeeding. First, I show them some chords or something in which they use both hands on every beat, so the notes aren't matching but the movements are. Then a bit of moving RH melody with the LH slow and stable, so the movements don't match anymore. Then maybe a gently moving LH accompaniment, and they're on the way. This might all happen in one lesson, or might take several, and I wouldn't push any stage because it's very important that they get physically comfortable and that they experience many combinations. If it takes a month, so be it, because they will love it; suddenly they're really playing the piano. When they can go back to written music-- something simpler but in the style of some of their rote pieces-- they will have a physical context in which to understand it and it will make sense to them.