Thanks for the suggestions, everyone!
They've met by chance three or four times now at the same park. It has been awhile, so my spouse had forgotten what she looks like. We didn't realize that it was her until after we left, else I probably would have found her adult and offered our contact info.
It turns out they are the same age, in the same grade, even in the same school district... just different elementary schools.
When we were leaving, she was exclaiming, "I really, really like you! I want to be best friends!" and he smiled and gave her a hug. She then whispered something in his ear... no idea what (and he won't tell me what she said). Too cute!
I'm going to have him write up a birthday party invitation to give to her the next time he sees her. That seems a little more concrete and easier for a parent to accept than an open-ended invitation.
