No magic bullet. If you have a "multi-tenant" schema -- a schema that represents multiple, independent sets of data -- you may be able to run each concurrent test in a different data set.
It is hard to be more specific about this without knowing more about your database, but here is an example. Consider an application as a service for managing employees. One instance of the service handles multiple companies, so the database has a company table, and all employee information is associated with a company. If you want to run concurrent tests, you might run each in a different company so that they do not interfere with each other.
If that isn't possible, you might consider altering your schema so that it is possible. Sometimes is makes sense to adjust your software so that it is easier to test. Think about how that might apply to your own application.