A method to tighten invisible set diamonds that are loose enough that they slide back and forth but not so loose that they lift up, is to use a #50 round bottom graver ground to a long narrow point. From the backside of the mounting cut a small bead from the support channel and press it tight against the pavilion of the diamond. One or two beads on each side of the diamond will generally hold it tight.
Before doing this make certain that the stone will not push up above the level of the other stone. To check this place a wax stick on the table of the stone and lift up.
As a last resort super glue can be used. Using the tip of a needle place only enough glue to fill the gap between the groove in the stone and the metal tongue of the channel. When done properly you should not be able to see any glue from the topside or from underneath.