For you I got:
Lapras, Aerodactyl, Houndoom, Swoobat, Venasaur, Galvantula
Swoobat and Aerodactyl are both part flying, but I assumed psychic and rock would be diverse enough. If you really don't want ANY type overlaps at all, I re-rolled and got Blissey just in case.
Update #1:
I made it...