Yes there is! The quickest way would be to buy an elixir. Most pet species have them. You can go to the Item Directory (sorry I'm on mobile or I'd post a link), and search for, say "celinox elixir" (substitute whatever species for celinox). That'll show you what colors they come in. Pick one, buy it, use on your pet.
Potions and the Zapper, the potions are pretty much a given of what color and species you'll get, the Zapper is random. Now, there's the Miracle Potions, you can use those to change the species but not the color (Miracle Potion) or the color without the species (Miracle Potion II) but those tend to be expensive.
Good luck.

Did some reading on this because I didn't know myself, but congrats- that's your new pet! There's always a chance that your pet will come back as one of the two Rift Amalgamations instead of a riftborn pet. You can change your pet back to the species it was before by using a common (insert pet species here) elixir. Elixir prices vary so sometimes it is cheaper to use a specific color on your pet instead of the common one.
Here's a link to a handy Subeta wiki!