based on Neil's own words posted on his Notes page. On 5/17/02 - The Grandchild Birthday Tour, Neil says "I've been able to be with two of my grandchildren on their birthdays. Elijah turned 2 and Benjamin turned 1 and I still haven't been able to wipe the smile off my face!"
Benjamin couldn't possibly have turned 1 had he been born in June. So, going with Neil's words, it has to be May.