Charles,
remember, that when the war of Northern Aggression started, the U.S. government was caught with it's pants down in that, it was not prepared to arm all the new recruits. There were too many soldiers to receive U.S. inspected arms. Procurement officers were dispatch to civilian gun dealers throughout the country & purchased what arms they could find, plus purchased firearms from foreign countries. You can bet that almost all civilian early 1860 Army Colts were carried in the war. A lot of 51 Navies & most other arms were also purchased plus add into the mix, private purchases of preferred sidearms, mostly by officers with money although there have been stories of enlisted men purchasing them also. I don't know if you ever had the chance to visit the Springfield Research Service website when it was online but you could see what serial numbers had been discovered through countless hours, months & years of researched visits to the National Archives. The reason that the site shut down was because of some dealers & researchers using SRS's researched numbers, then fitting in what guns they had (or information) into " range of serial numbers" & selling the guns at an inflated price to unsuspecting purchasers or people paying for the info. Because of this practice, SRS shut down it's site to prevent such practice & to protect it's interest.
It was a blow to those collectors & historians who used the info for honest purposes. There is hope SRS will return online to subscribers. You still can contact SRS & submit your number & if they have a hit, you have the option to purchase the info. Don't get me wrong as there are honest paid researchers that do their own legwork by going to the National Archives on their own & getting the info but you can be sure that some researchers used SRS for their own benefit but no longer have that luxury.
AS far as finding any info on your 51 Navy, I wish you luck but the chances are slim. In all the years I have been collecting antique firearms, I have found only one (61 Remington Old Army) that I got a direct hit on SRS & did find a wealth of info on the trooper who carried it in the 1st MO. Cavalry. It was a dream come true & comes close to hitting the lottery. You have to remember, that a lot of the recorded serial numbered firearms in SRS were probably destroyed in the war, sold as surplus after the war to other countries, or lost by other means throughout the years after the war.
Wylie Sword, known collector of documented firearms, once stated that less than one half of one percent of all Collectible firearms are documented & you can bet that those by serial number are less than that. Just enjoy your firearm for what it is & know that most likely that it played a small part in shaping this nation.