Mexican birth certificates can be obtained online. ActaExpress is an online service which specializes in providing vital records, such as birth certificates, to citizens both in and outside of the country.
The service requires that you fill out a request form wherein you must input the name of the individual whose birth certificate you are seeking, their date of birth, the state in which they were born and the state where their birth was registered. Other information can be provided such as the names of the birth parents and the city in which they were born, but those items are not mandatory; they simply expedite the process.
Once the form has been filled out, ActaExpress will require a small payment through PayPal. They then mail the birth certificate. It typically arrives within two weeks.