Hello, thank you for the question. It's a good one.
This wouldn't be a prenuptial contract because we aren't discussing marriage. This would be a cohabitation agreement. And it's a smart idea.
Firstly, people don't pay rent when they are in a spousal relationship. They contribute to the household expenses. You'll want a prenup to say that she acknowledges that the house is his and that the final responsibility to pay for the house and the associated taxes and utilities are his, and that she'll contribute X dollars.
So, how much should that X be? If it's half the mortgage and half of all the bills, then she'll have a good reason to claim that she should be entitled to a share of the growth in value of the home. More clear is that your son be responsible solely for what he'd have to pay anyway if she wasn't there, like the mortgage and insurance and municipal taxes. She should contribute to the bills that will be higher because she's there, maybe half of the utilities and phone/internet.
Also, the agreement should state that they are keeping themselves separate financially, and a short list of the valuable items that each is bringing into the home so that there isn't an argument later about who gets the couch.
This needn't be complicated or long, in fact it's better if it's short and clear. But it should still be done with the assistance of a lawyer because ideally you want her to sign off on her right to make a future claim to a share of the value of the home.
Does that make sense? If there's more to discuss on this topic then please reply. If I've answered you then I'd appreciate a positive service rating please.