Works perfectly with Kirkland brand red solo cups from Costco (lip diameter 4mm). I assume it should work fairly well with other brands, but if it's a little too large or small just scale it up or down a bit. I included a few models I made for my personal usage, but it should be pretty easy to add whatever letter or symbol you want to the top before printing. Printing in different colors is another option to differentiate the markers.

In testing it worked fine when Z height was reduced all the way down to 2mm, but 3mm is probably the sweet spot if you want to save a few grams of filament and reduce printing time.