He's so complimentary about the girl, and has them convinced that he is the way she is going to succeed
Just to play a bit of Devil's Advocate - Is there anything to suggest this isn't the case? Being difficult at work doesn't mean he's not the world's best tennis coach/whatever.
Nothing you've said screams grooming in and of itself. It's perfectly normal for a kid to have increased 1-2-1 coaching/teaching if they're excelling in something to the point that they're going to take it beyond a hobby. And it's perfectly normal for a coach/tutor/whatever to blow smoke up a parent's arse about how talented their kid is, either because it's true, or he wants to keep his fees rolling in.
So I guess it boils down to what else is setting off alarm bells? Is it just you and your partner's history with him?
To be clear I'm not saying that you're wrong or shouldn't report, but presumably something else that's happened here for you to go from simply not liking the guy to thinking he's grooming your friend's daughter.
You also say he's turned your friend against your DH...how? It seems odd that as her tutor/coach he would be having discussions with the parents about fall-outs at work with their friends. How does that even come up? Do other people know about your history with the guy? Have you raised the grooming concerns with any other friends?
I guess the worry is that if there is something going on, but you have no other evidence, it might not be taken seriously/dismissed as you having a grudge to bear, which would be awful.
As for legal repercussions - it depends. If there's nothing untoward happening and this report forms part of a pattern of behavior against him, it could be considered harassment. If you're going around telling people he's grooming someone and he loses work as a result, he could bring a defamation case against you for slander/libel, depending on how you're communicating it.
If you genuinely believe he is grooming a child though, none of that should matter. He can't sue you for anything you say while making a report to the police, and besides, that should be your main concern.