What kind of birth control can stop your period besides the shot?

Nexplanon: This is a match stick size "plastic" tube filled with a hormone that prevents women from getting pregnant. The tube is implanted under the skin of the upper inner arm. It releases the hormone at a steady low rate, so that it will last for 3 years.

Monophasic OCP: Monophasic OCP's can be used continuously for many months at a time. This will totally suppress your cycle. Withdrawal bleeding can be scheduled at your convenience. Seasonale / Seasonique were specifically designed for this, but others will work as well and are of course cheaper... Talk to your doc.