I asked the same question on another forum a while back and while there are lots of "opinions", I was looking for documentation. I never really got any good documentation. I was interested in what the "average joe" - i.e. not necessarily "cowboy" but travelers going by wagon across country, carried their loading supplies in. Many of the Colts, etc. - especially the Navy, were often supplied with bullet molds, flasks, etc. The general consensus was that since combuxtible cartridges were available, that's what was primarily used and the assumption was that since the military utilized leather cap pouches - so did civilians.
I disagree with those assumptions. A lot of Colt Navies were made and utilized by civilians - up into the 1870s and beyond. Certainly not everyone had access to ready made cartriges all the time. Caps were of course available in tins as they are today. Most men wore waistcoats (vest) in Victorian times - it was improper to appear before a woman without one but I'm sure some did. My guess is that many probably carried their loading supplies in some sort of leather or cloth "possible bag" = much like was used with percussion rifles. Caps may ahve been carried in a tin in a waistcoat pocket. Certainly some patented cap dispensers were utilized. Following the Civil War years, a lot of the surplus was bought up by such companies as Bannermans and sold on the civilian market. My father was born in 1908 and I heard him say several times that when he was a youngster, such things as Civil War haversacks were often purchased through various suppliers and utilized as "book bags" by school kids.
While cartridge handguns came in to use in the 18780s - Colts, S & W, etc. - thee certainly were a lot of C & B revolvers that continued to be used well up in to the 1900s. Let's face it - a person could mold their own balls, bulk black powder was still available and so were caps. My Dad told of those who still hunted with muzzleloading shotguns when he was a kid as it was cheap - well in to the 1920s and even during the Depression as times were hard. His father, my grandfather (born in 1867) still used his 45 cal. Ohio style half stock rifle in to the 30s - it worked well for him and that was all he needed to control varmints.
My reply really doesn't answer your question in regards to how caps were carried but I would have to believe that for the average individual, they did "what worked for them". Either in some sort of a possibles bag n a octet or in a tin, or their flask and ball bag in a coat pocket and a capper or tin of caps in a vest or coat pocket. They certainly would have had access to surplus military cap pouches so if they had a hlster for their handgun, they very well could have had a cap pouch for the belt as well.
I have shot BP for 50 + years - everythign from civilian arms to rifled muskets, C & B revolvers and even full sized Civil War cannons and mortars. I'm sure that "in the day" there were some that probably out of need and inventiveness, they fashioned some sort of belt pouch to carry caps along with a holstered handgun. They were just as creative as we are today. As far as suppliers for "cap pouches" out there. Dixie Gun Works, Track of the Wolf, various leather makers, etc. A good starting point would be to go to the NSSA website and look for sutlers. They are often sold on eBay as well. Some are made in the USA - many in India and Pakinstan. Like anything else - you get what you pay for. I do leatherwork as a hobby - gun belts, holsters, possible bags, etc but I dont't make cap pouches. I can't make a wood mold and set up and make cap pouches and possibly compete with those that are available for anywhere from $15 to $20. It's cheaper just bo buy one from a sutler. I even utilize a cap pouch to carry 38 cartridges in once in a while for my Ruger New Vaquero - the same way as the Army utilized Civil War cap pouches to carry 38s in during the early Indian War period.