Typically for most trees, stress will cause more suckers to grow. Basically what's happening is the roots/rootstock is try to grow more branches in efforts to reproduce.
Over watering, shallow watering, drought conditions, over pruning and over fertilization are usually the main caused of lots of suckers. Lack of pruning can also be the problem.
The best way to keep suckers at bay is to have a happy healthy tree. :/
If the tree is an ornamental cherry and has been grafted you might want to prune all suckers off at the base otherwise the tree might revert back to the parent plant over time.