On the top tang (equal in size to the lower one) it is stamped:

E Remington & Sons Ilion NY USA with Pats from May 30 1864 May 7th June 11th, Nov 12th Dec 24th 1872, Dec 31st 1872 Sep 9th 1873 Jan 12th March 16th 1874.

On each of the three stock bands there is a "U" stamped sideways. Under the barrel there is a "D" and a "P" stamped on either side.

The rifle is about 50 inches long.

How rare is this rifle? Its in really good shape.

here is a picture

In as much as I can tell from your picture, it looks like a conventional Spanish model with at least the stock refinished. Not rare at all, in fact its probably the most common military Rolling Block. If it has an octagonal breech section, its an Argentine M1879, and its all refinished, metal and wood alike.

The breech is round. Any idea what caliber it might be?

11mm Spanish?? This was the most common caliber aside from 11mm Egyptian. Black powder action Rolling Blocks had no caliber stamped on them so the only way to be sure of caliber is to make a chamber cast. Or, guess.