you could try for a home playdate.
Personally, I would not invite strangers from the park into my home unless or until we had established having mutual acquaintance(s), and I had researched them online. There are pedophiles in every neighborhood, people with alcohol or other drug dependency issues, child pornography issues, various forms of mental illness, etc, who do pass for normal. While some may find these issues to be few-and-far between, I am aware of top school districts who've employed individuals with one or more of these issues (and whose dismissal was covered by media). I would tend to advise erring on the side of caution.
