Please search for “Chorlton Park Tennis Courts” which should give you the following location;
The closest address is 30 Nell lane, Chorlton, M21 7SJ.
This will take you to the circle (marked 1) which has a very small public car park (only 7-8 spaces).
The area circled at number 2 around Sandy Lane, M21 8TZ can be a useful area for on street parking, as the pedestrian access to the park at the end of Beechwood Ave can then be used. However, please ensure you are considerate if parking in this residential area.