Therse are Deviant colours. Yes you can breed for them. While there is an element of randomness to it still, you can actively try to get specific deviant colours.
Please check out my guide here: Timain's Extensive New Player Guide and then in the table of contents in the first post click the Genetics / Colours and Patterns / Deviant Colours link. From there you can scroll down a little to get to the topic that covers Deviant colouring, although if you aren't completely clear on how the genetics work in this game, I would suggest to start reading at the beginning of that topic, since deviant colour breeding requires some base knowledge how to get certain pet colours.
I hope this will answer your questions, but if anything is still unclear, please feel free to send me a message or post here again.