Cell dye in red fluorescence spectrum
I've used the ThermoFisher brand of CellTrace dyes. Specifically, I co-cultured two populations of cells, one with CellTrace Far Red in the APC channel and another with CellTrace Yellow in the PE channel. My choice was in part guided by a product review by another lab touting the relatively low cytotoxicity of these products.

The protocol is quite straight forward. It's also available in CFSE and Violet, though I haven't tested those. These dyes are also optimized for lymphocytes, and so I'd recommend titrating if you're staining anything else.

The dyes are quite bright, and so there were issues with costaining APC-Cy7, for example. I ended up leaving my CellTrace dyes as the only markers on their respective lasers and stacking my phenotyping on the 355nm and 405nm lasers.

For compensation, you might just stick with cells, but in the product manual for CellTrace, however, it says:

"The CellTrace™ reagents readily diffuse into cells and bind covalently
to intracellular amines, resulting in stable, well-retained fluorescent staining that can
be fixed with aldehyde fixatives."

So if you use the ArC amine-reactive comp beads for LIVE/DEAD kits, you might be able to just make comp beads with those. I'll verify this when I'm back at work if need be, as I haven't done it myself, but it's a nice thought!