There is parking along the small street that runs between the park and some apartments. It is not marked or plentiful.
There's also parking on the street that runs down the side of that part of the park with the memorial with the fighter plane in it. It's next to the Rock Quarry Garden. Again, it's limited. I've been to a wedding there and it was a lovely affair. If you're not looking to park more than 15-20 cars the Garden is a nice place for small events.
Aaron Ochart is correct. However I have had no issue getting a spot since this little gem is never crowded.
Please pull to the park entrance and hand your keys to a valet parking attendant and enjoy the park at your leisure, sir. Free of charge.
Thanks! Your answer is awaiting moderation.