A couple of posters had negative comments, but everyone else made basically the same legitimate comment. Why wouldn't you just hand her parents a check for babysitting? It's very simple, creates a paper trail for taxes purposes, and they can give the money back to you later if they don't end up using it. The question of whether they want/need to be "paid" is rather beside the point, since you want the tax benefit and her dad already suggested that you to put money in an account for them.
People tend to get upset about perpetuating the gender-based pay gap by paying less or nothing for traditional "women's work" (childcare, teaching, etc) in this forum and try to suggest paying a fair wage to a family member who volunteers to provide child care, whether they want the money or not. It's a fair point, even in a world where many grandparents would/do love the privilege of watching their grandchildren and refuse any payment (such as my own). But I find that it's usually brought up by those whose parents have never offered that or could never imagine doing it themselves. Nonetheless, it's important to be introspective and consider why we don't want to hear the message (hint, it costs less).