I would encourage you NOT to make her do organized sports if she doesn't like them. I am not coordinated and at some point I really did not want to do team sports anymore. I would have been angry and humiliated had my parents forced me to continue. I agree that staying active is important, but there are many other ways to make this happen, as has been discussed here. Yoga class, swimming laps, regular hiking, biking to school, etc. Some people really don't enjoy organized sports. I agree that kids should try them out, but at a certain point I think they're allowed to say--hey, I tried them and I don't want to do it anymore.
I agree with you, but some people who are bad at team sports such as football, baseball, and basketball may be ok at individual sports such as tennis and racquetball -- this is true for me. In tennis, the net separates you from your opponent, and (given the speed at which amateurs hit the ball) there is a little time to think. Basketball calls for instantaneous reactions in a sea of people who are jostling you. The two sports call on different mental abilities as well as different physical ones.
My general advice is to expose a child to a range of sports and also to accept, as you say, that some children won't be proficient at any competitive sport.
