What AMD thinks: ATI Radeon
(300W minimum.) On the other hand, they boast that the card uses less than 25W peak. A high-end CPU uses 125W, but I'd expect less in a system with a 250W PSU. The power draw of all of the rest of the components shouldn't add up to much.
If the 250W PSU is in an appliance PC, see if its maker offered it with any discrete graphics cards.