I got my group coach a box of chocolates and my private coach a big chocolate star and a skating pin. If I had unlimited money I would spend more on them as they're both fab
My group coach gave me a little skate ornament for the christmas tree, and my private coach a little chocolate reindeer
Which was very sweet of both of them!
I don't know anyone in the UK who would give their coach a tip for xmas, but we're not as comfortable with tipping in general over here.