This page contains a neobadge creator, for 80 x 80 pixel images. This neobadge creator can display all pets and their colours, but it can only display happy and sad poses of these pets.
We also have another colour creator, one that displays 150 x 150 pixels images, and cannot only do happy and sad poses, but many more, like battledome poses. You can find it here:
Pet Colour Creator
There are countless of combinations that will not give you an image, like a Carrot Wocky. it gives a red X. This happens because these images simply don't exist, Neopets hasn't made a Carrot Wocky.
Below you can see the Neobadge Creator, you can pick species, colour and either happy or sad.