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I am writing a Steanpunk novel and am interested in having a "plausible" Union Steam Gun that would help turn the tide in an Alternate History American Civil War.

The gun can be either a machine gun type weapon that is operated by two or more soldiers or a hand held carbine or type weapon handed out to Union Cavalry.

My research found there was a Steam weapon called the Winans Steam Gun, that was also a centrifuge gun. Perhaps ideas on how to modify that to make it more effective.

By, the By, Thanks to everyone who answered my "Quick destruction Of a helium filled airship," question. You all are absolutely amazing, wonderful, creative thinkers. I am so grateful that you all choose to freely share your ideas and knowledge on this site. It is a wonderful tool and blessing for authors.

"Plausible", "Hand held" and "Steam Powered" are mutually exclusive terms when you're dealing with steam power in the age of steam.

Steam is big, it's heavy, if you're lucky it's self propelled, and even then the Winans Steam Gun didn't match the power of gunpowder weapons and its accuracy was terrible. If you want steam powered weapons, start with self propelled artillery and work your way up to tanks, but hand held is out of the question.

Traction engines did exist by that point, so having a steam powered base for your mobile artillery is possible. Making the weapon more effective is possible, but with steam it's almost always about boiler pressure, and at that point higher boiler pressure means a bigger, heavier, boiler and a bigger, heavier, furnace.

Let's try a look at the 'machine gun type weapon operated by two or more soldiers', because handheld isn't going to work, and I see no reason to drag the poor horses into this mess. The problem with the Winans Steam Gun is that it's just markedly inferior to rifles and and the Gatling Gun. So let's discuss Gatling Guns.

The Gatling Gun, by which I mean the one invented by Richard J. Gatling, and not the modern guns which bear the classification 'gatling', was invented right before the Civil War, with the intention being to 'reduce the size of armies and show the futility of war', of which it only accomplished one of those things. It had a few unique features, like the 'rotating barrel' concept, letting it fire faster without the barrel overheating, and used a gravity fed hopper. Now, here's the interesting part - it was hand-cranked. And where I see a hand-crank, I see a spot for a steam engine.

In other words, if you hook up the steam engine to the gatling gun, you can eliminate the need for a person to hand-crank the gun and possibly improve the firing rate - though not too much, because at a certain point overheating starts being an issue, but you could work through those problem by increasing the number of barrels (it started at 6) and reducing the caliber of bullet (started at .58), and the increased weight wouldn't be an issue, because it's not hand cranked, perhaps even up to a thousand rounds a minute. (Possibly - the highest it actually got was 900.) At which point it's not exactly hand-held, and would take a team of soldiers to use, and is only slightly better than the original Gatling Gun, but does work. Slightly.

Though if you want, you can stretch plausibility slightly by mounting the thing on a traction engine, add some deflective armor, and you suddenly have an impromptu half-track slowly charging at the enemy. It won't work on uneven terrain, get stopped cold by trenches (which were everywhere), and be a massive target for enemy cannons but just imagine these things tearing through a Confederate charge.

To prove a Mythbusters related point, scientists at MIT built a steam mortar cannon using technology and designs developed before 200 BC. This mortar could hurl projectiles with more energy than a modern .50 cal machine gun.

As @Separatrix rightly says, steam is an ugly beast that is difficult to fully weaponise. However, the invention of a small and (relatively) portable mortar cannon would allow your army to respond agilely to combat scenarios.

The invention of the mortar (especially one more powerful than a cannon) would allow your Union to lay down cannonfire faster and more frequently than the enemy, so your army's tactics are very difficult to respond to because you could have projectiles flying at the speed of sound at any moment. The stealth advantages of mortars over cannons is also something to consider.

Mortars were reinvented in-promptu at The Siege of Vicksberg in 1863, and proved remarkably effective. In fact, the result was a decisive Union victory that many consider to have been the war's turning point. Any side that developed this technology first (and in a more scientific way than right on the battlefield) would be a serious threat.