Can monitors sit on a TV console instead of stands?

They will sound better on stands — more space to breathe and more flexibility in placement.  

@czarivey , we all know Tony meant feet not ".

(1meter room ha ha)

Sounds like I might be better off with small floorstanders over monitors then?

Yes?, no?  ???

@labguy Definitely. You will feel that. I’d say to go with at least 10" woofer speakers (or doubled woofer) or add sub-woofer or a couple -- one per side. 

Whatever you do, put springs or some sort of decoupling solution under the speakers to reduce vibrations.

1st, solve your center channel. Just below the screen works best to anchor the dialog to the screen.

Temporarily put books below the monitor, solve the height for both you and your mate/kids, ....

(not too high for neck looking up, see glare/reflections this/that height. To keep my center just below the monitor, I made a riser for the TV to raise it the height of the temporaty books below my monitor so that I could use this Klipsch Center Channel (no rear vent!)

Next: front left and right either on the console, or floor standers.

On the console: The monitor might be a bit more than 24" high (depends on monitors leg design), and then, add the height of any riser below that. Thus narrow speakers on the console could be narrow/tall i.e. 10" max wide, +/- 30" high. Again, Klipsch has speakers that are highly efficient, passive or self-powered. (You could actually use a pair of one of their center speakers vertically).

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Imaging: when no center channel info is present, the left/right information wants to present it’s content to a wide area, i.e. 3 people wide on a sofa. The ability to alter the toe-in can be a big advantage, not only for 5.1 say, but also when listening to 2 channel stereo, so think about a solution, i.e. felt pads on bottoms of L and R speakers.

A sub? I would start without, then add if needed. My sub, not for all content, just enough to add Jurassic Dino Stomp when present.