A penny for your method: Nutator

This one requires a little ingenuity on your part (and perhaps some craft, duct tape, construction, and/or welding skills).
A nutator (AKA nutating mixer or rotating mixer) is a gently rocking/rotating platform useful for continuously and gently mixing samples. They are particularly useful if you’re doing bead-binding sorts of operations – like binding biotinylated oligos to streptavidin-coated beads. This is a pretty common workflow for lots of tasks including one that is increasingly useful… target enrichment (AKA sequence capture or solution hybridization).

Anyway, if you have a nutator, then that’s super. I don’t, and they’re far more expensive than they should be. So, I offer you a very inexpensive solution: a rotisserie kit. The kit nets you the all-important spit pole and is a one-stop solution, but you can also buy just the motor and get the rest of what you need at a decent hardware store.
Once you have the kit in hand, you can get fancy if you like (or, if you can weld). If you don’t want to get fancy, string this bad-boy up between two of the thousands of styrofoam coolers you have in the lab. Make some styrofoam squares with holes in the middle (the spit pole goes though these), and affix your sample to be nutated to one side of the square (ensure you’re using decent tubes that close well). Repeat for as many samples as you need to nutate. Make more squares if needed. This also works for strip-tubes and well-sealed plates.