If its important to you, and you’re capable of having grown-up conversations as a couple, then there’re probably lots of ways to figure it out. Start by taking the pressure completely off by telling him that you understand that it makes him uncomfortable and you’d never want to pressure him into something he’s not fully consenting to (can you imagine if it was a 20F posting that her older boyfriend keeps trying to push her to have sex in a situation she feels uncomfortable in?)

Then try and find out what is actually the source of the issue for him, and if he wants to, work on that. If he deep down struggles to believe that your parents are cool with this guy banging their can’t-even-drink-in-a-bar* aged daughter then maybe your parents have to be more direct about giving their approval. I had a gf who’s parents had noisy sex when we were staying over and whose dad made super weird jokes like “we want her back in one piece <wink>” when we said goodnight. It was deeply awkward, but I certainly didn’t worry about them judging us for having sex.

Similarly, if it just makes him feel self-conscious and that doesn’t make him feel very sexy, maybe you can start doing (consensual) minor sex stuff during the day while he’s visiting. Or spend time during the day watching TV or chatting in your bedroom with the door shut. And once he’s confortable spending time in your bed and in private, and he sees that your parents don’t judge him even though you could have been having sex, it’ll be easier to accept an overnight. And tbh, when staying in someone else’s house it’s much easier it have sex during the day when people are busy and there’s noise from TVs and stuff, than at night when any noise feels very obvious.

But the main thing is to respect each other’s boundaries, and realise that some things take time.