It is not easy to come by a foreign, English-language newspaper in Manzanillo. You will occasionally find the Guadalajara Reporter available for purchase. The Guadalajara Reporter is also available by subscription, online.
You can find news local to Puerto Vallarta at Banderas News and they also report on national concerns. The News, from Mexico City, also has an online subscription option. The Yucatan Times offers news targeted for those on the east coast and covers national concerns as well.
There is a list on the page below to a number of publications, some print, most online and not certain that all are currently-available but you may wish to look around and report back if you find a publication worth mentioning here.
This one also lists some sites as well as Twitter feeds in English, in Mexico.