Connaught's fine. It's a town park, not a recreation ground; anyone for tennis who needs a net and not a couple of jumpers can surely fling their balls and racquets into an open-top and drive to a club somewhere.
Building a car park there would destroy the park and reward bone-idleness. I walked there (and back) this morning (5 mile round trip), and plenty of people were walking up Connaught Road and Park Lane to get to the main entrance.
With tadpoles in the pond, robins and chiff-chaffs in the trees, cherries in blossom, all that's needed is a refreshment kiosk to replace the one that used to stand here: