I'm courting a lady who wants to play a one-on-one game where she  plays a demon magician. She wants them to have decent survivability, along with some minor healing powers. In addition, she wants a deceptively chonky, actually dangerous flying rabbit familiar that gives the PC their power.

I'm thinking a reskinned Celestial chainlock with fiend flavor, or Fiend with DHealing Light, but I don't know. What would I use for racial stats? She wants a tiefling rogue ally, so there should be a difference. What about the familiar?

Reflavored celestial is the best choice for class. The demon part is the hardest thing to get down, especially if they want a distinct difference from the tiefling. If you have Mordenkainen's tome of foes, you should also have the rules for variant tieflings. There should be a different tiefling type for every archdevil. If that isn't good enough for you (or is still too devilish), a feral tiefling is also a good option. In terms of other options I have racial traits for demonic characters, but I think it would be a good idea to check out these options before asking me about those. 

For the familier, a quasit.

Hope this helped!