If I did it it would have to be through Society6, not Etsy since for Etsy I'd have to make the t-shirts in advance and store them in my apartment. Society6 is print on demand, so it's where I do tshirts.
Checked out your store, I might have to get myself a Starbucks Hoodie when I can afford it!Love your stuff, I really hope to see a t-shirt like this in the future! Love your work, you really are very funny, and I eagerly await new stuff.
Well I tried www.spreadshirt.com once before. I bet if you search around, you'll find one that will work out for you. Be careful with the colors though. they have to be CMYK, or else they'll print out all wrong. I sadly experienced that -_-
If you open your image in Photoshop and go to Image-Mode-CMYK it should make the adjustments you'll need to make the printed colors you want. After saving it in that mode, whatever shirt site you're on upload it on to there.