The obstacle to making a river is usually getting the water uphill to begin with. Regular cloud seeding of moist air currents that would otherwise head out to sea? Modifying land albedo to change airflow patterns? That's all dubious, but I can't think of any other ideas for starting a new river with new water.

If you've got a situation where the water you want to flow is already "uphill", then the technology is simply digging, and if you wanted to do enough of it you could make whole new seas.