You really have 3 options: plant a second sweet cherry tree, graft a limb on your current cherry tree, or take your chances and hope one of your neighbors somewhere near by has a sweet cherry tree in their garden that will pollinate yours. Not knowing where you live, I have no idea how likely this third option is, but if many of your neighbors have fruit trees, it is possible.
You mention that you don't have room for another tree, but would you perhaps be able to find room for a small one? Compact Stella is a small sweet cherry. It grows to 10-12 feet tall naturally, but can be kept smaller with pruning. I have had no trouble keeping mine at about 8 feet tall, so I don't have to get a ladder out to pick. Stella is a pollinator for Bing. Even if you do not have room for a full-sized cherry tree, maybe you could find a spot to tuck a Compact Stella into?