How is that you have say in the font being used? How much say do you have? Assuming you have full control, here are a few thoughts:
Generally, san serif fonts are considered to be slightly more challenging to read than serif, though it's debatable how much of a consideration that is in picture books, which are often read to children rather than read by them... But that's not the only aspect I'd look at.
It's difficult to make a suggestion in the abstract, as the right font for a book depends on so many things. Do you want it to look modern or classic? Light or heavy? Playful or serious?
I'd suggest pulling some favorite picture books off the shelves in your library and browsing to find a font that "feels" right for your book. Then tell the publisher to look at that as an example, and leave it up to them to figure out exactly what font is being used in that book (their designer should be able to do that). If they can't find that specific font they should be able to find one that feels like it.
Good luck!