Are there places you can order custom teapots similar to the way you can order custom t-shirts?

No teapots, but for a glimpse of a similar business, see CafePress.com.

Here are some things you can design and sell on-line, for brevity I omitted most of the clothing:
* Christmas ornaments
* mugs
* steins
* sigg water bottles
* greeting cards
* note cards
* postcards
* calendars
* clocks
* posters
* framed prints
* pillows
* keepsake boxes
* tile coasters
* framed tiles
* aprons
* Christmas ornaments
* t-shirts
* sweatshirts & hoodies
* posters
* bumper stickers
* mugs
* calendars

What about those places that were all the rage about 5 years ago? You go in, pick out your greenware, paint it yourself, and then they fire it for you. There were several chains of them, but damned if I can remember what they were called.

Hmmm:

http://www.paintyourownpottery.net/
http://find.mapmuse.com/interest/pyo-pottery

If it’s the design of the shape that you’re interested in, I’d find a local gallery and start chatting up a potter. They may be will to let you order a design piece.

That would be perfect! Perhaps someone else can remember for you @syz!

For a less expensive alternative, depending upon the complexity of the design, you can do it yourself.

Any craft store ( Michaels, Hobby Lobby, A. C. Moore, etc. ) should have ceramic paints which can subsequently be baked in your oven for permanence.

Going along with @syz, Color Me Mine is another paint your own pottery place.

I would also recommend taking a look around esty. It’s a site for selling and buying handmade and vintage items. There are a lot of very good ceramists and many of them will do custom orders.

Yes. I forgot the site name, but is is very good.

You could make your own teapot. Just buy some clay at an art store, shape your teapot, and then find someplace where you can rent the use of a kiln for an hour or so. (You’d need to use the kiln twice—once for a bisque firing and once after you glaze it.)

It probably wouldn’t be any more expensive (probably less expensive) to make it yourself than it would be if you ordered a custom teapot from a ceramist. And its cool to when the finished product is something that you designed and made yourself.

I made this teapot last year in an art class. It isn’t very difficult, just time consuming.