Printing cups and sleeves
I don't know of any that do small orders at any reasonable cost. Look around online, there are a ton of specialty marketing companies, just try and get a reccomendation from someone first.
There is also a cheap, almost as pretty, way to do it yourself. Have a rubber stamp made with your logo, etc. on it, buy a stamp pad in a color you like, and when it is slow in the shop your employees will have something to do. Sleeves are easy to stamp and cups aren't bad once you get the hang of it.
Also, you could have stickers made, which can be done pretty cheaply, and sticker your cups.
I prefer the stamp pad.