Yes you can setup your own payment provider.
You can see below how that works:

1)
Create a coupon and select claim method "make a payment".
Select as payment method: "custom URL".

2)
Enter here the URL where you want to develop your own payment integration.
Example: https://www.yourdomain.com/pay.php

3)
Consumer view:
The the consumer opens the coupon and on the payment page we will redirect the coupon to your URL:

Example:
Coupon url: digicpn.com/p/abcdef/ab12de34fg56gh89
Note: We pass here the unique coupon session ID in the URL. Example: https://www.yourdomain.com/pay.php?coupon=abcfef&couponid=ab12de34fg56gh89

4)
You can now develop the payment process on your page.
After a succesful payment you can make and API call to inform our platform that coupon session ID was payed.

API ENDPOINT:
You need to pass the operation=CLAIM method. A succesful payment is equal to a claimed coupon.
Optional you can pass custom fields (customfield1 untill customfield7) to store additional information (eg unique payment reference, payment method, etc)

Note : you can find your API credentials in your account (integrations -> API)

After making the API call you can redirect back to our coupon URL. example: digicpn.com/p/abcdef/ab12de34fg56gh89
The consumer will see the coupon was payed and he can save/redeem it.

5)
Result: the consumer has exact the same flow as our integration payment methods (PayPal/Stripe) but processed through your own payment provider.
The flow to save/redeem/validate the coupon is exact the same.