I've dealt with a similar situation except the kid I was teaching wasn't very exceptional, just determined and a hard work ethic, and it was more of keeping him out of trouble and not getting involve with gang life and drugs.
What I did was talk this kid up to his parents, saying he has a lot of potential that, with hard work and "support" from his parents can go far in the sport. As I was saying this I would interject every now and then about getting him better equipment to further "enhance" his progression as a "positive" selling point.
. Remember, be subtle about it but make sure you get it in the back of their head and pretty soon you'll see new sticks and shoes in his hands.
My kid's parents were really poor so they could only afford him discounted tennis shoes. I was just happy they were "tennis" shoes! I just lent him one of my racquets, and eventually when he made 1st Team All League I rewarded him with the racquet and a 2nd identical one for a back up.