I guess it all comes down to how you define "knocking" someone down. If you define it as "they hit the ground after being shot," then yes, even small .22 rounds can "knock you down" under that definition. This could occur for a variety of reasons: the brain stem or spinal cord was disrupted (CNS wound), a bone was struck (structural failure), the subject was off-balance when hit (gravity assist), and/or psychological reaction to being shot. In this case, the bullet hits and the man (or woman) hits the ground. If that is what you mean by being "knocked" down, then yes, bullets can do that.
So can arrows, slingshots, spitwads and bumblebees
Another definition that many people use, however, is "kinetic energy knock-down"; i.e., the kinetic force imparted by the arriving bullet literally knocks the person being shot off his or her feet. This is, in effect,"knock down kinetic power" relative to a non-living, non-thinking hunk of flesh and bone that weighs, oh, about 200 lbs or so. It eliminates the CNS and psychological elements of shooting living beings and turns it into a physics problem. In that case, almost no conventional handgun rounds and some rifles will not "knock" the dead weight very far. They may punch a hole in it, tear it up do damage to it, but really don't kinetically knock the weight very far. Of course, the bigger the round, the more "knocki-down" power you get in this context. A .45 ACP probably won't move a dead body too much, but an 88mm shell definiteloy delivers a LOT more kinetic energy and it definitely wil send a body flyingl. Variables go up and down the scale as velocities and bullet weights vary.
I think the combat-oriented question is not whether or not a "can a bullet knock you down." I mean, if it can, so what? If it can't, so what? How do we use this information? In the first context, many people do hit the ground after being shot only once, and often pretty much instantly. This doesn't mean they were "knocked" down by kinetic impact, however. By the first definition it's a knockdown, but by the second definition it's not.
There is also a matter of time involved here that must be specified within context. Does the definition mean "instantly" or several seconds or minutes later? Obviously, if they go down minutes later, the "knock down" under kinetic criteria did not occur, but even if they go down instantly, kinetic force may not have been the likely cause.
I think the question--if properly focused and accepting either definition--should be "can you count on bullets knocking a person down?" Again, I'd have to clarify what is meant by "count on," which is this case, you, as the shooter, are you willing to bet your life on the fact that your bullets will absolutely cause the bad guy to hit the dirt every time consistently?
To me, the answer here is a definite NO. Your shot may or may not "knock" the purp down (depending on the defintion used). You cannot count on it in either case, however. There are too many vairables in a gun fight for any absolutes. Some people go down with a skin scratch, others don't go down instantly even after being shot in the head by a .357 Magnum at point-blank range (there are documented police shootings that verify this). So, to me, this becomes an academic argument either way at this point. From a combat perspective, does it even matter? A more pragmatic question would be "do you shoot the bad guy once or keep shooting him until the threat is neutralized?" I mean, how it affects your tactics and survival is what is useful. Not the academic argument. We hear the same kind of nonsense all the time in the old "one-shot stop" debate. Interesting perhaps--we all love to debate--but hardly all that useful.
In terms of the academic arguments, I think the common concept being debated has mostly to deal with the Hollywood image of a shotgun blast or .45 slug blowing a guy clean across the room or sending him flying through the air. Shotguns and .45s just don't do that That's a fact. For that kind of "kinetic" effect, yeah, Newton's Laws have to apply. But for all of the others, like falling to the ground, not necessarily. Newton's Laws still applly--they just don't apply to the cause. I don't think the statements that "it doesn't happen" are really so much a matter of short-sightedness as much most folks' iinability to specify the conditions associated with their premises, and then articulate them in a way that that supports their conclusion.