Gen 3 starters:
Treecko: Pokeball, Park Ball
Reasons: Getting your starter/Breeding, Pal Park
Torchic: Pokeball, Cherish Ball, Park Ball
Reasons: Getting your starter/Breeding, Events, Pal Park
Source
Mudkip: Pokeball, Park Ball
Reasons: Getting your starter/Breeding, Pal Park
Gen 4 starters:
Turtwig: Pokeball
Reasons: Getting your starter/Breeding
Chimchar: Pokeball, Cherish Ball
Reasons: Getting your starter/Breeding, Events
Source
Piplup: Pokeball, Cherish Ball
Reasons: Getting your starter/Breeding , Events
Source
Gen 5 Starters:
Snivy: Pokeball, Cherish Ball
Reasons: Getting your starter/Breeding, Events
Source
Tepig: Pokeball
Reasons: Getting your starter/Breeding
Oshawott: Pokeball
Reasons: Getting your starter/Breeding
Note: You cannot breed starters into a Cherish Ball because the Cherish Ball is not passed down. To get a Pokemon in a Park Ball, you have to transfer from Gen 4.
(Note: The above Pokemon that have Park Ball listed can only be caught with a Park Ball, it will not keep the Park Ball once you catch it, it will be in it's original Pokeball.)
Hope I helped!
Source:
I've listed them above
and knowldge