Track, Cross-Country, or tennis.

Jui jitsu

Climbing

Climbing and gymnastics can be competitive, and in any solo athletic activity you can compete against yourself trying to beat your time or complete a more difficult trick or course.

Are you not happy with her not participating in a competitive sport, or is she asking for that? I wonder if more for the competition aspect or for the team aspect. Asking because there are other ways to have competitive or team experiences besides sports, e.g, academic competitions, tabletop gaming clubs, Scout troop, robotics team.

I think suggesting tennis or fencing might be good. Both are more energetic than golf, and field hockey is probably going to be a no if she didn't like lacrosse or soccer.

Some other thoughts:
Girls on the Run
circus arts
volleyball
basketball

What might be helpful is to look at what your local parks & rec, YMCA, or school clubs offer starting at age 9 or 10. Then she'll be more likely to find herself among other kids who aren't good at the sport yet either, as opposed to say swim team or soccer where kids may have been participating since they were 5.

Anonymous wrote:Fourth Grade girl who had rejected soccer, swimming, dance, and lacrosse. Not naturally athletic but had a lot of energy. Enjoys climbing and gymnastics, but hoping to find a lightly competitive sport for her. She tends to be self-conscious about not being good at something in front of others. Not great hand-eye coordination. Tall and skinny build. Field Hockey? Fencing? Tennis? Golf? Any insight?

Fencing might be a great fit. Start with foil.

My kid like this did cross country running and swimming in HS. Team sports but really about setting individual goals and working towards them.

Cross country, rack, swimming, fencing, horseback riding/polo

My 10 year old who sounds similar just started rock climbing and she seems to be really enjoying it. Our Y has classes and then after you "graduate" from the classes you can join the rock climbing team. I didn't even know there was such a thing!

Volleyball. 5th grade is actually a good time to pick it up.

Field hockey is very similar to soccer, pretty much the same field positioning for a little kids, so if she wasn’t comfortable with soccer, she may be intimidated by field hockey, particularly since sometimes you have the ball flying at you. I would try to get her involved in tennis, it really helps with the hand eye coordination. Although there is a bit of a learning curve, so if she gives up quickly, that could be an issue for you. Golf is another great idea. If you have access to that, since it’s an individual sport and she may not be as intimidated as in the group sport setting. What about Swim?

climbing and fencing are the usual recommendations

Running.

Running. Can you sign her up for Girls on the Run?

Tennis or Swimming

Fourth Grade girl who had rejected soccer, swimming, dance, and lacrosse. Not naturally athletic but had a lot of energy. Enjoys climbing and gymnastics, but hoping to find a lightly competitive sport for her. She tends to be self-conscious about not being good at something in front of others. Not great hand-eye coordination. Tall and skinny build. Field Hockey? Fencing? Tennis? Golf? Any insight?