The Rainbow Fountain is located in Faerieland, and is one of the places you can change the style of your pet. It's not that easy to get painted from there, you have to wait for the Fountain Faerie to give you a quest. The item she asks for will probably be very expensive, which is why you should see if it's worth it or not. Once you give her the item, one pet will be able to get painted. Her quests are also very rare. If you visit the fountain when you have not been given a quest, the faerie will state that all the magical power is currently used up.