Quite frankly my recommendation is not to buy cheap controllers. You get what you pay for. I know this is just a little box for kids to play on, but cheap controllers often fail right out of the box or shortly after you start using them. Then you wind up replacing them and spending more money anyway. It's not worth the headache.

I would go with a pair of wired controllers like the logitech f310, which currently goes for about $20. If you insist on using wireless there is a wireless version available that uses the old 2.4 Ghz connection.

If you really want bluetooth, I think the best possible option you can go with is the 8bitdo zero 2. They're colorful and compact, perfect for small hands, and they're only $20 each.
https://www.amazon.com/dp/B081HML6MP

I swear by 8bitdo and have been using their products as my go-to controller for a few years now. Their flagship controllers are more expensive but worth the money in my opinion. The SN30 Pro wired is around $30 https://www.amazon.com/dp/B08Y9RC49N?th=1 but the bluetooth version is around $45, so probably more than you want to spend here.

My suggestion for this project is to use wired controllers to save yourself the hassle, but if you are committed to bluetooth, the Zero 2 is probably your best bet.