You may wish to use one of the large, well sign-posted tourist car parks close to the Promenade or there are two car parks closer to the Winter Gardens.
A multi storey car park is available within the Houndshill Shopping Centre. This is about 150m from the Coronation Street entrance (lift access to the main areas of the Winter Gardens building) or about 300m from the Church Street entrance (ground level access to the main building). The postcode of this car park is FY1 4NY and costs £2.70 for 2 hours (pay on return).
Open air, ground level parking is also available on the corner of Alfred Street and Adelaide Street, about 200m from the Church Street entrance. The postcode of this car park is FY1 4LA and it costs £3.50 for 2 hours (pay and display).
You can find all other parking options near the venue on the Parkopedia website.