Here are 140AP combos.
Forward O, O, S, Down S, Forward S, Up S, Forward O
Forward O, O, S, Down S, Forward S, Up S, Jump quickly, Forward T.
Forward O, O, S, Down S, Up S, O, S, S
You can also use O first but you'll get a different max AP instead.
Of course you won't always be using max AP combos. Only when possible. Pretty simple to string combos with Parappa though after you learn his moveset. Great character.