Lyman and others show many smokeless loads for the Trapdoor in their special trapdoor loads section. I wouldn't do it opting instead for real black powder, which is what the rifle was designed for.

I have been shooting smokeless exclusively in my trapdoors for about 35 years. I make it a point to stick to published data and keep the velocities down to black powder equivalents or lower. My standard loads are 22 gr 4759 with a 500 gr bullet, 23 gr 4759 with a 405-440 gr bullet, and 23gr Accurate.  Arms 5744 with a 405-440 gr bullet. I have also used 19.5 gr of 4759 for a light load which is accurate and pleasant to shoot, but not quite as accurate as the faster loads. 
I keep saying I want to shoot some black powder, but never have the time. Good luck! Joe S

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The old tried and true load in this area is 24 grains of 2400 with malt-o-meal filler behind 405 grains of lead.  The cheap 459 hollow base Lee mold works better for me.  Be careful and visually inspect after powder for double charging with smokeless before adding filler!!!!!

James

I have never used "fillers" in any smokeless loads. trapdoor loads and pressures for different smokeless powders are listed usually by the powder manufacturers. Trapdoors need minimum pressures to prevent problems. I have shot 405 grn without a problem. Black is  uch more fun though.  Gunner'

Joe, sorry for the implication, did not mean anything by it. I just have not heard of using that for a wad. I do not use wads on smokeless, maybe I will give it a try. We can always learn something new everyday.  Thanks  gunner'

The use of wads with smokeless powder is, possibly, the most misunderstood component of reloading today. Some say I never harmed or rung my barrel then there are the horror stories like the idiot who blew up a stainless steel Sharps copy. The action stayed together but the barrel couldn’t contain the stress anymore and grenaded. 
Charlie Dell proved how ringing happens and it has little to wad it’s self and everything to do with the placement. There are some wad materials that can contribute to the problem such as Dacron and of coarse you can overpower any steel by overcharging. But by far the main cause of ringing and eventually failure is wad placement.
     Most shooters fixate on the wad or the material the problem occurs when the powder is held tight against the base of the case and the resulting explosion becomes a plug of pressure that travels up the chamber and meets the bullet base. The resistance of the bullet to start moving causes a pressure spike. Think of a shaped charge. If the powder has sufficient force a ring will be formed in the metal. Most rings are formed a tiny bit at a time until they become visible. Leaving the wad .050” to .100” off the powder will allow the powder to slump inside the case and change the way the pressure flows up the chamber. 

40 Rod