What years were US 2 dollar bills printed with a red seal?

Red-seal $2 bills were issued from 1862 to 1963 so there are lots of different dates and series combinations. There's a full list including values at the Related Link.

In general red seals indicated that the bills were United States Notes, a form of currency issued directly by the Federal Government instead of by the central bank. Some older silver certificates and Treasury notes also used red seals before colors were standardized in the 1920s.