Gee, I like the idea, but it has pitfalls. Business cards can be very personal.Let me lay out some thoughts.
I like the idea of the 'scheduled lesson' on the back, that's very professional.But how often can a coach find a pen or a pencil to write a schedule down. In my experience all they have in their pockets are keys, big markers, tissues,, a cellphone, and sometimes gum, a glove without a mate, or a beanie baby. Maybe include a pen with his name on it.
I think if the card front was simple like a name and a contact, even then you'd have to be careful. Suppose your coach has given you a contact number he only gives to a few students. I think it would be safest just putting the name and the contact information that's publicly available (like from the rink's or his website).
As for skills sets, look at it this way. Suppose your coach is well known. Maybe he's taken skaters to regionals or Nationals. He won't need to puff himself up on a card. And if he's not well known, he might be sensitive about how his information is framed on a card.
Even a motto can be a touchy issue. I don't know how old you are, and I'm assuming you are female and your coach is an adult man, but when it comes to mottos (as with other things) there's a gulf between men and women. Things a woman might find perfectly acceptable or even bland ("Skating is a sport for a lifetime." ) you'll get some off the wall response from a guy ("That's girly"). Hey, I don't even begin to understand them and I've spent nearly 40 years dealing with military men and engineers.
I do caveat with the fact that i'm viewing the skating world with the eye of an outsider. I've read a lot of skater's bios on rink sites, and some of them make me cringe. However, this seems to be the profession norm. So, what do I know? I work in a profession where good practice is a card with a name, 3 numbers, 5 email addresses and a logo.
There's other options. One skater had personalized post it notes made up for her coach with name and contact number on it. I thought that was good too.