There's quite a few options for a back-up gun besides a .22LR derringer that I personally would feel more comfortable recommending, but if that's what you've got your heart set on:
1) Avoid Davis derringers, and likewise, Cobra Enterprises derringers(the Davis design marketed under a new name). Cheaply made, with cheap materials and shoddy workmanship. In .22LR the cheap construction probably won't affect the durability much, unless you're gonna shoot the thing as much as your primary gun(i.e. several hundred rounds per year).
2) American Derringer Corporation makes some very nice guns, with lots of choices in calibers and design features. They can be on the pricey side, though.
3) Bond Arms makes excellent, durable guns, which are probably the most user-friendly derringers on the market - the only thing I don't like about them is how big they are. I don't believe Bond Arms offers their guns in .22LR, though.
4) You'll have to shop the used-gun market, but a very good choice would be the old High Standard double-action derringer - you don't have to thumb-cock the hammer, just point and pull the trigger.
Now, with that said, my question is: "Are you looking for a .22LR derringer, specifically, or are you just looking for an ultra-small back-up gun in general? If you aren't married to the derringer idea, please consider, for close to the same price, one of the Beretta .22LR pocket autos(more shootable, higher capacity), the North American Arms mini-revolvers(5-shot capacity, even smaller than any derringer available), or even the Kel-Tec P32(more effective caliber, better ergonomics, lighter and thinner than ANY other gun available, PERIOD).