You should be walking over to a downed ally and trying to stabilize them with a healers kit. This act would not even bring them back to their feet but would simply stop them from needing to make death saving throws. It's something that any class could do.
I think it would be fine to be able to administer a healing potion to a stabilized ally by walking next to them and using an action. That ally should already be stabilized though. Letting someone gets down in combat should be punishing. The stakes are so low with the current system that the tension in combat is completely undermined.
