I can give you a couple of numbers for a specific year.
The first pair of numbers are from the shop of Sam Hawken.
According to the 1820 Industrial Census - Sam, while working in his shop in Xenia, Ohio, built 21 rifles valued at $420 and made $300 in rifle repairs. He had one "hand" (employee) who was paid $20/month.
So "maybe" he could produce 3 rifles a month if doing no repairs or other work (a guess) - the average would be 1.75 per month.
Now onto the 1850 Industrial Census when Sam was in St. Louis, the year after Jake's death.
He had four (4) employees on the payroll ($120/month) and between the five of them they produced 100 "handmade" rifles and 20 shotguns valued at $2700 ($22.50 average cost per gun).
In this case they produced, on average, 10 firearms per month or 2 per employee "on average".
The second set of numbers is further spanning and come from the shop of John and Caleb Vincent.
(side note - John was primarily a farmer with gunsmith business being secondary according to notes I have).
Anyhow, here are the number for years 1848 thru 1863 (when it appears John stopped building and Caleb set off on his own):
1848 - 18 rifles, 1849 - 3 rifles, 1850 - 2 rifles, 1851 - no rifles, 1852 - 7 rifles/1 pistol, 1853 - 7 rifles, 1854 - 14 rifles, 1855 - 8 rifles, 1856 - 11 rifles, 1857 - 8 rifles, 1858 - 10 rifles, 1859 - 13 rifles, 1860 - 1 rifle, 1861 - 5 rifles, 1862 - 5 rifles, 1863 - 4 rifles.
They also built 20 spinning wheels in that time frame and repaired an untold number of rifles.
(side note - from the TOTW catalog you might think that a "VINCENT" is the essence of an Ohio rifle. From their numbers they were neither common nor prolific compared to many other Ohio builders - something to consider when an Ohio rifle comes to mind)
Notes I have from Journals Caleb kept indicate strongly that for every rifle they "built" they restocked about 3.
So they were busy, but rifle building took a back seat to repairing and restocking existing rifles.
This kinda makes sense given the years they operated in.
Plus, John served during the civil war with a militia unit which is possibly a reason for the drop in production from 1860 onward.
John is not known to have built a rifle after 1863. Caleb kept horrible records, so post 1863 numbers for Vincent rifles is pretty much non-existent.
They had no employees so their numbers reflect one or two workers (depending how much time John spent running the farm on any given day).
Their best year, 1848, with 18 rifles looks similar to Sam Hawken's numbers of 1820, with one employee - so possibly indicative of speed of production for a pair of workers.