does not appear to list any, though there might be something out there.
As with most things Streets of Rage it is probably easier to program this in one of the various fan remakes, beats of rage or something like that where you can do say the levels of 2 with the setup/mechanics of 3.
Still it would not actually be the worst thing in the world to add as a getting used to assembly hack though if you were inclined to go for the original game.
I would probably start by finding an infinite health cheat. This should give you the location of the health for a character.
Now you would set a break on write to the health (can't remember if this will allow you to suicide by doing the power moves without health, no great issue though as you can just refill the health thanks to your new cheat) and do the always costs some health power move (you could do the other if you have an enemy nearby but why make it hard, you might have to go back to it afterwards though).
Whatever then takes the health will be as a direct result of the move being performed so you would want to add an extra check to for some value you set elsewhere in memory that acts as a charge counter.
The elsewhere in memory is presumably a timer of some form. This would mean you probably want to add a value every frame (so you are presumably finding the vblank routine) until the required number (or take away until it reaches zero if that makes more sense for your setup) with the special move resetting it.
Alternatively you could give a limited number of "free" special moves per round (find whatever refills health between levels and get it to add to this counter if you are doing this)/game this way.
The hardest part would then be adding a graphical element as that would involve going into the graphical side of things. Graphical aspects would mostly be icing on the cake though. Might be an option to do something like alternate colours for the health bar or something when it is charged without having to go do something nice with extra sprites.