I really like the other kinds of balls but I could never get a fossil Pokemon with another. Is there any way?
No. Not legitimately outside of events
Unfortunately, no, you can't have fossil Pokemon in any ball except a Pokeball (unless if you hack). Unless, of course, if you get one from an event, which would come in a Cherish Ball. I know, it sucks that they can't be in an Ultra Ball or Luxury Ball or whatever kinds of balls you like, and I hope that this can finally, somehow be changed in Sun and Moon.
Hope I helped! :)
Yes just make sure its a boy fossil Pokemon then breed it with a Pokemon with the same egg group (Female) And the ball you used to catch the mother will pass down to the baby hope I helped!