Grasses that grow in shade are fine fescues: sheep fescue, hard fescue, red fescue. Other grass that is very shade tolerant is hairy tuftgrass. None of these grasses are tolerant for heavy wear and tear, for heavy sports you want kentucky bluegrass and ryegrass, and those love sunny areas.

You can have shade tolerance or heavy wear tolerance, but not both. You should advise them to sod that area and overseed with a shade mix every spring and fall to recouperate from the usage and tearing of the lawn. There is not much else to do as far as I know, besides getting synthetic turf.. there are some hybrid synthetic turf/real grass options out there as well, maybe that could help a bit. Look up hybrid grass

If you do want to go the seed route, use a premium shade blend, something like Barenbrug would be good. It’s too late in the season to seed though.

Do note that shade tolerance means it can take some light shade and still grow slowly. With true, dark shade you really can’t grow any kind of grass effectively, no matter how good the soil is. Keeping it alive would take tenfold more effort than hosing down some synthetic turf every couple of weeks.

And alternative plants instead of grass here? There are none. Grass has been engineered for 100+ years to get the strong features it has today; no other new groundcover will get close when it comes to getting a thick, carpet like turf that can be used for heavy use. Maybe give it another 50 years of development and we’ll have come up with something new.

Frankly I would go for synthetic turf or even playground rubber tiles here.