Providing newspapers to each occupied guestroom is wasteful, and lots of otherwise green hotels follow this practice. Being a green hotel doesn't mean giving up hospitality, and hospitality doesn't justify being wasteful.
Take stock of how many guests really want to read the newspaper and distribute that many. Habitat Suites in Austin, Texas, has determined that about 1/3 of their guests enjoy having the paper. It will take some research and effort for you to determine how many papers to provide. Consider these options for making newspapers available to the guests who want them.
Habitat Suites saves unused newspapers to use for cleaning windows and glass. Newspapers can also be used in the gardens as mulch, keeping weeds down. Or if you are composting food scraps, you could also build a "worm farm". Worm farms use newspaper as a worm medium; instructions can be found on the Internet. And of course, newspaper that's not used for anything else should be recycled.