Does DiscLabel support printers that print directly on CDs and DVDs, like the ones from Canon, Epson, Primera and Dymo?

Yes.

For paper printers that also have disc trays, or otherwise support direct-to-disc printing, see DiscLabel's built-in Help, or view this article: http://www.smilesoftware.com/help/DiscLabel/printdirecttocd.html

For disc duplicators that also print on disc, DiscLabel supports
- Primera: https://smile.helpscoutdocs.com/article/154-how-do-i-print-to-a-primera-bravo-disc-printer

- Microboards:  https://smile.helpscoutdocs.com/article/155-how-do-i-print-to-a-microboards-printer