Dónde consulto los Registros de Nacimiento de los pueblos de Durango, México?

Here is the catalogue for Durango, Mexico: https://www.familysearch.org/en/search/catalog/results?q.place=Durango%2C%20Mexico

Here is the FamilySearch Wiki page for Durango: https://www.familysearch.org/en/wiki/Durango,_Mexico_Genealogy

It looks like you can find birth records at Ancestry for the years 1861-1930. This is a fee site. Here's the link to the collection if you have access: https://www.ancestry.com/search/collections/60397/

FamilySearch might have births in their microfilm collections (meaning they aren't indexed, so it will take a little more work). You can read about and access them by reading number 2 in the FamilySearch wiki page.