I want to add bitcoin to my website for users to pay with but is the method im trying to do even possible?

My site is a subscription service and im looking at accepting other payment processors as paypal and these credit card services keeps trying to screw me over by letting people chargeback my service after a month. Then i thought is there a way to still allow users to purchase my subscription but have them automatically billed and my payment received in Bitcoin without me having to send a bill and wait for them to pay? Ive already looked into bitpay and coinbase but none of them offer subscription services for merchants just auto billing. Anybody know of anything or any other ideas?