Audino, Musharna, Solosis line, Gothita line, Leavanny, Alomomola, Budew line, Clefable, Hattena line, and the Ralts line (possibly excluding Gallade). My reasoning is that all of these Pokemon have been used by the Doctor Trainer Class.
Edit: Thanks to Blue & Gary for reminding me of Comfey, and ☆SleepyDreepy☆ for Wigglytuff.
Notes: Audino and Alomomola are each stated to be excellent healers. Leavanny cares for Sewaddles and other Pokemon. Musharna and the Solosis / Gothita / Hattena / Ralts lines are all stated to be empathetic. The Budew line can have Natural Cure. Clefable can have Magic Guard.
Hope I helped!