The North Country Library System offeres free access to old newspapers in a system similar to the one at Fulton History but focuses on newspapers from the seven counties the system serves from its base in Watertown, New York. They are: Oswego, Jefferson, Lewis, St. Lawrence, Franklin, Clinton and Essex counties. The search and layout are similar but does feature some newspapers not available in the other site.
NNY Historical Newspapers
Again, access to the digital newspapers is free to anyone at the above link.
However, there are some additional features such as access to the pay site from Heritage Quest containing Census and Digital Historical Books that are free to patrons of the system with a North Country Library System borrower's card. Those without a library card from a member library unfortunately can not access Heritage Quest. Check with your home library to see if it offers Heritage Quest access. Some systems and individual libraries do make it available to library patrons with an active borrower's card.