One of the best methods for preventing starlings from entering purple martin house entrances is to prepare especially adapted plates and adding them over the existing hole. It may be necessary to cut out the existing hole to accommodate the chosen plate. It is important to mount the plate as close to the floor as possible to make it difficult for the starling to enter. The suggested arrangement is 1/8 inch above the floor. The suggested height of the entrance hole is 1 3/16 inch. The chart below indicates the various plates the can be purchased from various vendors both as prepared entrance plates that can be mounted on the house or doors that already have the desired hole.
Unfortunately, there is very little that can be done to keep other songbirds from entering the holes. The House Sparrow will readily enter both round and Starling Resistant Entrances.
More information on the history of these entrances can be found under the topic: