The nearest, large car park is the multi-storey at St Peter's on Augusta Place (use the postcode CV32 5EL). It costs £3 to park here for up to 3 hours, and it's a 10-12 minute walk to the theatre at buggy pace.
There are car parks closer to the venue, but these are much smaller and spaces may be very limited. Please allow plenty of time to make sure you can find a place to park!
Visit Parkopedia to see all the available parking options near the Royal Spa Centre.