To change colors of outlines, you will need the color wheel, which comes with Golden Token. The Golden Token is a paid item in the in-game shop which allows you to have infinite pet space, every color of the rainbow, transparency, and many more perks for as long as it is active.
The perks from color wheel only last as long as it is active. If you wish to continue to use these perks, you will have to purchase another Golden Token.
If you have petz beyond your storage capacity and you lose your token, your petz will not be lost! However, you will not be able to pix any more petz until you have more space.