In 1855 colt made the Colt New Model Revolving Rifle. It was produced until 1864. Other rifles at the time were mainly just bolt action rifles, even if they had magazines (such as tubular ones), they were still bolt action requiring people to pull back after every shot which reduced rate of fire obviously. Meanwhile, a revolving rifle only requires a simple hammer (the top thingy trigger thingy, I think that’s what it’s called) to be pulled back. Why weren’t more revolving rifles experimented on? Why weren’t they used and more produced, especially when revolvers were so prevalent for so long and therefore parts could be reused. Or, why weren’t revolvers converted into carbines? Such as the Luger or C96
Revolving rifles did see occasional use - see the Battle of Chickamauga during the Civil War - but had several issues that prevented mass adoption.
For military reasoning, the biggest issue first and foremost was ammunition. As counterintuitive as it may seem, military leadership across the world was concerned about any system that would increase the fire rate of the standard rifleman due to fears over soldiers "wasting" ammunition. These fears would impact the adoption of breech-loading infantry rifles and last all the way until World War 1 in the shape of magazine cutoffs on rifles. While this is hard to understand now, logistics were a huge issue in pre-industrial armies, so a massive increase in fire rate may aid in individual engagements, but it could be a major liability during the campaign as logistics were increasingly strained. Chickamauga was a good example, where the revolving-rifle armed 21st Ohio did manage to leverage its better firepower to hold its ground, but in doing so they ended up burning through all their ammunition and ended up surrendering. For armies like the US Army, which expected to be operating in remote frontiers with sparse infrastructure, ammunition conservation became paramount and the resistance to repeating rifles became fairly extreme. A good example is the postwar US Cavalry, which had their repeating Spencer carbines replaced with single-shot Trapdoor Springfield carbines. So for military use, much of the resistance wasn't so much aimed at revolving rifles specifically, but rather repeating rifles in general. Similar institutional resistance also impacted adoption of lever-action rifles on a mass scale and even slowed the adoption of magazine-fed bolt actions. For magazine rifles, a critical feature that most military customers looked for was the ability to easily regulate the fire of the soldiers through the use of a magazine cutoff to keep the rifle as a single-shot until directed to engage the magazine by officers. Systems were developed for both vertical box magazines and tube magazines, but it wasn't a feasible option for a revolver.
Other issues more specific to revolving rifles also made it a less optimal choice once magazine rifles were being seriously looked at. Early revolving rifles like the Colt New Model Revolving Rifle were cap and ball revolvers, which were very slow to load. Safety issues existed with revolving rifles due to the hot gases escaping from the cylinder - an issue with nearly every revolver to this day. Hot gases escaping from the gap between cylinder and barrel were dangerous to shooters and could injure hands and arms supporting the front of the gun, and often times these gases could ignite the charges in the other chambers. Even once brass cartridges had come into common use, the safety issue of the cylinder gap remained. Compared to contemporary repeaters, revolving rifles also had several functional drawbacks. Due to the nature of the design, the cylinder of a revolver ends up being significantly heavier than an equivalent-sized magazine on a bolt-action or lever-action rifle. Each chamber in the cylinder has to be strengthened to withstand the forces of firing. While this isn't a particularly significant increase in weight for low-powered pistol cartridges, rifle rounds are significantly more powerful and thus would require significantly stronger (and heavier) cylinders.
Ultimately, by the time magazine rifle trials started up across the world in the late 1880s, bolt actions had long been established as the best option. A few lever-action designs did get developed and submitted to various trials (most famously the Winchester 1895 and Savage 1895) and even the odd pump-action rifle for the British trials, but no revolvers.