This might be a reach, because I'm not sure if 9 is still a playground age or not, but Paddington Gardens is a really nice green space with a playground attached. At after-school time, it is positively overrun with kids, and not just little ones. I am fairly sure the little girl who ran into me this afternoon (they were playing tag in the rain and I was dashing for cover) was about that age. If she's an outgoing type, it might be worth swinging by. It's just in back of Marylebone High Street, you can get in off of Paddington Street or Moxon Street.
Also, not sure if she's a sporty type, but another pack of similar age-ish little girls were all wearing tennis camp t-shirts. I know there are lots of sports camps/clinics/lessons that are going on in Regent's Park -- might be worth a look.