You have a big job ahead of you. The LDS church offers on-line indexes of births, marriages and burials, so you should look for the name Avendano for each state of Mexico separately: Sinaloa, Chihuahua and Sonora. You may find something that will help. All information from the LDS is free.
However, I discover that most information that I needed was not indexed yet. Therefore, I had to browse through image after image of records also available through the LDS. This is an intensely time consuming process. Maybe 1000s of hours.
On the same screen where you do an indexed search, scroll to the bottom. Select the item including Mexico. Then select Mexico catholic church records. Then select the city/district of interest. Then select the parish. Once you have it a list of files will appear. Select one to view actual images of the original church books.
Hope this helps. With extensive time and effort you should find information about Rosario and his family, too.
Eduardo Nissen Padilla