"Any other newspapers"
is correct as it appears in the Blue Azar (Understanding and Using
English Grammar, Prentice Hall Regents, 1999). "Any other
newspaper" is also possible.
Other is an adjective that can modify a plural count noun (other
newspapers) or a noncount noun (other information). If other
is meant to modify a singular count noun, such as "newspaper," it must
be combined with "an-." Thus, "another newspaper" is possible.
In addition, there is another way to combine a singular count noun such
as "newspaper" with other; that is to place any before
the adjective other. You can say "any other newspaper," so this
phrase is also correct.
"Any other newspaper," however, means something a little
different from "another newspaper." "Any other newspaper" means
"not even one" and emphasizes the meaning of "zero." "Another newspaper"
means just one more in addition to the one or ones already mentioned.
It refers to one more of a kind and continues a list.
The difference in meaning between "any other newspaper" and "any
other newspapers" is slight: "Any other newspaper" refers to
"not even one newspaper - not even the Washington Post or The
London Times or Pravda or one other newspaper," thinking
of them individually and as a possible alternative to The New York
Times. "Any other newspapers" would refer to all of the possible
newspapers in the world, and in Alice's case in Sentence 11 on page
143, could be many newspapers, not just one.
For more insights on any, please see the message "Any:
Singular and plural nouns."