The likely problem is the replacement cog is thinner than the stock cog.
Old school cogs were all for 1/8" wide chains.
A few years ago the boxmarts started using 3/32 drive lines for some coaster brake bikes (old 10 speed width).
Some 3/32 cogs have little stampings adjacent to the hole to take up some space on the driver.
But many 3/32 cogs don't have those offsets so they fit loose on drivers intended for fatter cogs and will rattle around. You can probably feel it move around with your fingers while stationary or if you just bounce the rear end up and down.
You can add a spacer. Some try cutting one out from a cottage cheese container lid, that's about the correct thickness (1/8 - 3/32 = 1/32" thick). Sturmey Archer 3 speed hub spacers are a bit too thick.
Another issue with cog swapping is the diameter of the hole. The Sturmey Archer size is different from Shimano size, the two most common sizes. If you use a larger diameter cog on a smaller diameter driver, the 3 little ears won't engage the driver by much so they are prone to slipping (and rattling).
You can run a 1/8" chain on 3/32" cogs and sprockets (chainrings) okay but you can't run a 3/32 chain on a 1/8" cog or sprocket.
Rick
