Hello! And welcome to Chicken Smoothie.
The easiest way for users to find pets is the
Free adoptions forum You'll find people quitting and wanting to give away pets, giveaways, adoption centers, contests, and all sorts of other free ways to get pets.
You've already found the monthly adopts. The first of each month a new batch of pets is released for users to adopt and watch grow. They are babies now but they'll grow. I'll link
this months pet archive if you'd like to see what they may become. If you end up with duplicate outcomes of this months pets you can also swap them with other users
Here to complete this months pets. However
The trade forum is good for general trading.
The Pound is also a good way to get pets. You can find it under the "adopts" tab on the menu bar near the top of the page (unless you're on mobile where it has its own tab on the top bar). It opens at random times throughout the week but the pound page does have a timer so you'll know at the earliest six hours before it opens. There's also the lost and found run out of the same page where you can get items to dress up your pets.
If you enjoy making art you could also set up an art shop,
Linking the whole art shop forum. In the appropriate branch people create shops for art, characters, or custom coding for signatures and forum posts in exchange for pets, items, or C$.