The original standard "service loads" - 480 grain bullets and around 80 grains black powder for both Snider-Enfield and Martini-Henry - have pretty stout recoil, as clearly evidenced by Guns' photos .... However, he was effectively shooting nearly a full rifle load in a M-H cavalry carbine .... which even the War Department wouldn't let its soldiers do .... they delayed issuance of such carbines until a reduced carbine load was adopted.
As Sir Charles indicates, lighter loads will significantly reduce the recoil, and still be effective for most GAF shooting (i.e. except perhaps for any "long range" shots.) I have not yet tried any round ball loads, but many people report excellent results with such loads in Sniders .... especially full-length 3-band rifles, which have very "slow twist" 1:78 rifling. However, I tam of the view that a ball iof only 58 caliber range or so is too small for best accuracy, since the progressive depth Enfield rifling grooves (.013"deep at the breech, .005" at the muzzle) result in an effective average major bore diameter of over .590". Accordingly, most folks reporting consistently good accuracy with round ball loads use at least a .590" diameter ball, or even .600" ..... Chamber dimensions on these old girls vary somewhat, and that may determing how big a ball you can use and still have your cartridges chamber fully.
A .600" round ball will only weigh about 325 grains, and a reduced powder charge of perhaps 60 grains black powder should produce a pretty mild recoil.
In a "straightwall" case like the .577 Snider. something as simple as cream of wheat or cornmeal can be used as a filler between the reduced powder charge and the projectile .... however, you need a fairly good quantity of a suitable black powder lubricant in the load somewhere, to keep the fouling soft. I use a "grease cookie" under the bullet - i.e. a wad of home-made soft lube (50/50 mix of olive oil and beeswax melted together) about 1/4" thick, sandwiched between cards punched out of milk cartons - but many people using round ball loads seat the ball well into the case mouth and then fill the top level with their lube .... rather like lubing the chambers of a cap and ball revolver.