I am replaying the FFVIII again because I need to get better junctions and reexperience the game without leveling up but it is difficult considering that I enjoy Lionheart, Ultima and the Omega is always a t LV.100. Is there to gain AP without leveling up?

Boss battles. Because they don't give EXP.

Card mod also IDX.

Later in the game, Catuars. They give, like, 1 exp, and they give 20 AP apiece.

You want this here-- it's a really good FAQ on this subject-- http://www.gamefaqs.com/console/psx/file/197343/19814 (It's also really well written and rather entertaining to read.)