Something we found out petitioning for a park was that the authorities are rarely interested in peoples views that aren't rate payers, or their children. It's not their job to provide amenities for surrounding people, so unless it's a paying facility there's no benefit in it for them, all you're saying is "you'll spend £xxx allocated to our residents and its going to get worn out by residents from another area."
You might be better off writing to local authorities nearby that have successfully built skateparks and getting them to provide a written statement as to the success and popularity of the park.
There does seem to be a genuine shift (or call it a trend) where they are starting to sit up and take notice of something other than football and tennis courts, and it sounds like you're getting on well so good luck with it, it'll happen eventually!