Wow! So she doesn't live in what you consider a "safe" neighborhood, and you're concerned that there is no place for them to play outside?
I would let my child go on the condition that they play INSIDE since I am not comfortable with the neighborhood.
And the boyfriend - what does that have to do with anything? Do you automatically distrust a boyfriend? Wasn't your husband your boyfriend before you married him?
But you trust the coach. Don't you recall the big to-do about the couch who molested those boys in college just recently? Just because he/she is a coach doesn't make them any different or any better or any more trustworthy than anyone else.
I would be honest, but then again my honesty would be they can come, but only if they play indoors because I am just not comfortable with your neighborhood as opposed to your honesty which is they can't come because I don't like your neighborhood, they can't go outside and I don't trust your boyfriend even though I don't know him. Hmmmmm.....