First, Nicole, welcome to DC. I'm sure you'll like it here. Regardless of the questions you might ask, you'll always get an answer or two, or three, or....
Anyhow, just how pink do you want to make the cake? The first thing that came to my mind was basic food coloring, either liquid or paste. Failing that, I would imagine the maraschino cherry juice would do the trick to make the cake a faint pink without giving too much of a cherry flavor. Reason says that the more juice you add, the more likely the cake will be flavored. I don't have any experience using maraschino cherry juice to tint cake batter, but I can assure you, there IS someone on this site who does or who can explain the science of same.
Best wishes. You will most certainly get an answer.