If you’re in some profession where you routinely need to apply one of two types of tape, Uline’s Multi-Roll Dispenser has you covered, plus one. But as you can see, the design is terrible:
Obviously the tapes oughtn’t be so close together. A better design is this Double Tape Dispenser by Benchmaster Woodworx:
However, that’s got a heckuva lot of parts. Which brings us to this third approach, by Japanese office supply company MDS Co.:
I’d love to try that last one out in person, to see how frustrating it is or isn’t to use, but I can’t find a U.S. distributor for it.