I just noticed that the left-field grandstands are different in the OP's postcard than in one of the ones I posted. League Park was rebuilt before the 1910 season (one of the PCs I have, shown below, pictures a construction crew working on the pitcher's mound on the date 9-28-09, marked in the lower-left corner). It was during this construction that double-decker grandstands were added. So, based on that, the image in the original OP was taken during a season before 1910.
The previous owner of the PCs in my collection researched many of the photos and identified the pitcher throwing in the outfield (above) as Jim Baskette, who played for Cleveland in 1911-13. The player pictured (above) in the car is Ray Chapman, who played for Cleveland 1912-1920. So I think it's safe to say that these postcards were either issued over several years, or the manufacturer used photos from several seasons.
Of course, this attempt to narrow down a date of the OP's postcard is all for naught if it is from a different series/manufacturer. Below is a scan of the back of one of my PCs, all of which are the same.
