The PS2 version of The Sims 2 Pets has no cheat codes for relationships. The "boolProp testingCheatsEnabled true" PC cheat is absent. You must build romance the old-fashioned way—but efficiently.
Create a "Romance Room": Place 2 pet beds, a toy, food bowls, and a stereo. Lock the door for pets only. They'll autonomously socialize there while you do other things.
Patience + treats + cohabitation = puppies/kittens in 2–3 in-game days.