I recently managed to create a Cartographers guild so that I could try and get some wild pets easier. However, it's been roughly a week and each time I look there are only gryphons and cockatrice showing. I was wondering if the game just shows that there are pets in that area (represented by just the two picture)? Or is my thing a little stuck? I've not seen a Puma, Unicorn or dragon at all.

I believe this is the thread I initially picked this up from, but in short:

If for example all your dens currently house cockatrice, then no other animals will appear (that use the same dens), until the current inhabitant has been captured and the den becomes available again.