Short answer: No, you cannot have children in The Sims 2 Pets for PlayStation 2.
The PlayStation 2 port of The Sims 2 Pets is a stripped-down experience compared to its PC counterpart. It lacks the core "Create a Sim" and family gameplay systems that define the main series. Instead, the game focuses exclusively on interacting with and caring for pets. You’re limited to pre-made Sims and animals; there are no mechanics for creating new Sims, aging, pregnancy, or raising children.
If you want the full life-simulation experience—including generations, babies, and family trees—you’ll need the PC version of The Sims 2 (with or without the Pets expansion) or a later entry in the series.