I think a good partner for Heihachi is anyone who can get in, since with my experience with Heihachi, once he gets in, he can pretty much stay in (since while his walkspeed is terrible his dash is pretty good for keeping up with someone who’s trying to run away).
I think Ken could make a decent partner, since his air-tatsus and step kicks can help him get in, his multi-hitting shoryuken leads to safe tag-ins, and if necessary he can zone (not very well but better than nothing). By the same token I think Ryu could work as a partner as well, but trying to safely tag-in Heihachi with Ryu probably won’t work out as well.
And @Sho 'Nuff, I think Raven could be an excellent partner as well. He seems to get in pretty well, has excellent mix-ups (which can lead to safe-tag ins I think), and he can run-away as well if you need to. As for gems, I think you should give Raven 2 meter gems and a power gem (or 3 meter gems), and use the ones that activate when you connect with x amount of special moves and normal moves. As for Heihachi, I give him power and speed gems. Personally I give him the power gem and speed gem that activate when your partner connects with a launcher, and then give him another power gem (or speed gem) that activates when he connects with x amount of special moves or normal moves, since when you tag in Heihachi it should only be when you get in. If you aren’t in with Heihachi, chances are you aren’t going to get in.