If you mean CS pets, only official site artists can design pets. You can post ideas
here though!
There's also the
adoptable oekaki and the
user-made adoptables. Here, people can design anything they want, and adopt it out to other users. These aren't the same as pets, and won't be added to your account or anything. You can create your own adoptables, or find someone who's looking for artists and apply to work with them.