The Shulchan Aruch, OC 94:5, writes:
Suppose someone is sitting on a boat or wagon [and saying sh'mone esre (amida)]. If he can stand up when he reaches the point of bowing, he should stand, so as to bow while standing. Likewise, he should take three steps.
The Rama adds:
That is, although he's sitting for the entire prayer, he should nonetheless stand, if possible, in order to do the bowing and stepping correctly. However, if he can't — for example, if he's riding an animal, he should back the animal up three steps, and it will count for him as if he himself took the steps.
(That's my own free translation; don't rely on it for practical halacha.)
It seems to be that the last case, "if he can't — for example, if he's riding an animal", arguably would apply also to someone in a wheelchair: he should move the wheelchair backward and forward three "steps" (short movements). Indeed, I have seen someone in a wheelchair do so, though I don't know whether he had any source for it. On the other hand, since a wheelchair, unlike an animal, takes no actual steps, perhaps such movement backward and forward is meaningless.
Does anyone know of any posek (halachic decisor) who addresses whether someone using a wheelchair should move it backward and forward at the start (and/or end) of sh'mone esre?