Do you already have citizenship? If so then the easiest way I have found is to make an appointment for a card at the centre in Manzanillo (sorry can't remember its name but the directions are given when you make the appointment). https://ine.mx/credencial/

You take all the required papers and go. They will tell you when to come back to collect it.

The other option is check for when one of the mobile stations comes to town (in Melaque someone announces it on local groups, or posts a notice on the delegacion doors) and then go and queue. You have to go early and have all papers with you ready to go as they only process a small amount. Then again go back when they tell you.