OP is looking for recurrent payment options not one time. As far as I know coinpayments and other offers one time payment only. Honestly speaking, I have never seen a recurrent payment using Bitcoin yet.
I think coinbase offered subscriptions some time ago not sure if they still do.
The issue with a subscription / reoccurring transaction and Bitcoin is the you don't pull BTC / crypto, the sender has to send it. If none of these services offer a subscription the best way to go about it would likely be to assign every user an address and run a script that checks for payment. Every month the user has to check to see what this months payment amount is and then send it to the same address, the script checks periodically to see if the subscription was paid up and continues to provide access to the service if it was or adds time to the account.
Otherwise if you use one of the other services, they are just acting in a similar manner to paypal or a credit card company where they will take x USD/BTC/LTC/etc. from the user and transfer it to you.