thewarning, Yes. There are photos in Dean Thomas's Round Ball to Rimfire Part Two. The bullet for the Greene Rifle, not carbine, does look like an Enfield but with a blunt nose and no base cavity, a solid base. The dimensions for the bullet are diameter .545 and length 1.00. A bullet for a breechloader would be larger than the bore.
Dean Thomas has a photo of a possible Greene Carbine bullet and cartridge that are similar to a Sharps but there is a ? by the photo so I assume that even the acknowledged authority on Civil War bullets may have some doubt about this one. A Greene carbine bullet would be very rare.
As I said, in the old McKee and Mason book, the long Enfield bullet for the .54 Mississippi Rifle and Lorenz were listed as Greene Carbine bullets but later research has proven that wrong.
You may wish to check Amazon for a copy of Jim and Dean Thomas' A Handbook of Civil War Bullets and Cartridges. This is a great quick reference and not expensive.