I believe Browning made and marketed a recoiless single barrel trap gun a few years back; but I've never shot one, or was interested enough in the gun to learn how the systems operated (perhaps you can locate a Browning catalog from that era and read their description?). I did see and handle an example of this gun at my local gun store; I found it a bit heavy and asthetically unappealing to my personal tastes. Back in my registered skeet shooting days I saw a number of competition guns fitted with a hydro-coil device, a shock absorber installed inside the buttstock; but todays modern technological advances in shock absorbing pad materials have just about obsoleted these older and more expensive recoil taming methods.
The Browning Recoilless was a 2 shot semi-auto for shooting doubles, and they did have very little recoil. They had 1 major problem though, if you shot real heavy loads in them they just would not hold up, and most of the trap shooters I know always have some real heavy loads for shoot-offs.
There was also the "Ljutic Recoiless Space Gun".
Sounds like a joke, but it's for real. However, it's no longer in production.
It was probably too expensive and it looked pretty bizzare too, but it predated the Browning design. Google it, you'll see.
BTW, Ljutic is still in business making high end trap guns, the cheapest "off-the-shelf" model going for about $6K. The custom made ones start at about $20K and go up from there. Good stuff if you can afford it. (I can't)