Here's what happens to Teddy Lupin after being born, in Remus' words:
"Not much hair. It looked black when he was born, but I swear it's turned ginger in the hour since. Probably blonde by the time I get back. Andromeda says Tonks's hair started changing colour the day that she was born."
And here's what Tonks says to Harry:
Metamorphmagi are really rare, they're born, not made.
I'm concluding that, however rare, there is some gene that Tonks has and is passed on to Teddy. The wiki, though, only lists Tonks and Teddy as Metamorphmagi. Is there any evidence of past Metamorphmagi in Tonks's family?