I don't know prices or if it is much different for goggles, but if you haven't, at least look at Zenni. I helped my mom get measurements and select a pair of glasses about a month ago, b/c she was told by her eye doctor that the glasses she already had were adequate (some really old ones, but she had cataracts removed, so her vision is much better and her newer glasses are no longer the right prescription for her), but the older ones are, well, old, and not in such great shape--even though the prescription is ok.
She was reluctant to go shell out over $400 for a pair of progressive lenses at an eye doctor's office. She ordered through Zenni, and got a pair (in the mail, in less than 2 weeks) for about $50 (including shipping). She loves them! And she couldn't be happier that she saved over $300.
Now, I don't know if goggles will solve all the issues for your son (never tried them myself, never did a sport with a helmut after I started wearing glasses really.. hats, yes, helmets no).
But, if you are game, you could price a pair online and try them.
Otherwise, contact lenses are really the best solution for sports. Your peripheral vision is perfect with contacts, and no fogging up lenses from sweat, or dripped sweat making smeared, blurry lenses to try to see through.
The eye doctor can give him a trial pair and see how he does.
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ETA:
Yes, you will need certain measurements like PPD and bridge size, arm length, etc. But Zenni's website has a frequently asked Q section and walks you through where to find or how to take those measurements yourself. Don't be scared of that part. We measured my mom's PPD with a sewing measuring tape (only one in her house that had mm markings on it), and were even ordered progressive lenses! She says she can see perfectly out of them.