I got to be Eevee. It's hard work being a normal type, but learn attract through a tm and you can totally blitz the game. Then I got red rescue team and I was Eevee again!
Also, I have the Mystery dungeon guidebook. Here's the posible pokemon you can be, also, some are girl or boy only.

(Boy=Impish/Girl=Hardy)

(Boy=Docile/Girl=Calm)

(Boy=Hardy/Girl=Brave)

(Boy=Jolly/Girl=Relaxed)

(Girl only, Docile.)

(Boy only, Timid)

(Boy=Naive/Girl=Jolly)

(Boy=Sassy/Girl=Quirky)

(Boy=Hasty/Girl=Sassy)

(Boy=Calm/Girl=Timid)

(Boy only, Brave)

(Girl only, Naive)

(Girl only, Hasty)

(Boy=Lonely/Girl=Impish)

(Boy only, Quirky)

(Yes, Psyduck.)(Boy=Relaxed/Girl=Lonely)
These are all the possibilities. Also, the questions change, locking you completely out of some pokemon on some sets of questions. The boy/Girl Q always appears.
P.S, I did not use my guide to get eevee both times. I was truthful.