For birth control pills, most gynecologists recommend Yaz or otherwise known as Yasmine. It's available at pharmacies and requires no doctor's prescription.
For the birth control shots, I haven't heard of a medical center or hospital that administers them but I can ask the gynos at the hospital about them.
As for the Depo-Provera, I suggest you read the safety pamphlets about the shot here at
MHRA . Of course, this shot cannot be administered without visiting a gynecologist and reviewing the medical history of the patient.