If you email anyone and do not get any response in a week, you send another e-mail. Because obviously the e-mail was either forgotten or overlooked (most likely) or never received, or is being deliberately ignored.
24- 48 hours after sending that second e-mail, if there is still no response, you contact the person another way. Unless of course the issue is urgent. In that case you forego the second e-mail and contact the person another way immediately.
E-mail is usually the most appropriate and is often the preferred means of communication in this kind of circumstance. If a coach prefers another means of communication that is their responsibility to communicate that preference.
It is never polite to "pester" anyone, of course. But gym coaches are not kings or queens and parents are not their subjects. They should be just as available for questions and concerns from parents as any teacher or any other adult instructor the child is in close contact with. Do piano teachers instill this fear? Why so much special deference for gym coaches? I've never seen anything like it. It's weird.