1. none of them is tired
2. none of them are tired
This is a chronic problem in English. Technically, "none" as a pronoun is singular, but when it is followed by a prepositional phrase with a plural object, a plural verb is commonly chosen. It is almost speaker's choice these days. I say "almost" because absolutely no one can object to a singular verb (except when "none" is modified by "almost") and some will object to a plural verb.