Admin can set discount rules based on Payment Method.

For making this discount rule select Discount Rules tab.
Now choose Payment Rules
Now you can choose Add New Rule.

Fill Rule, Restrictions and Validity tabs accordingly.
After saving the rule it can be seen in the given table below.

Now you have to give permission to your rule to give discount on the product you have chosen.
Click on the Setting Tab.
Check Payment Rule as shown below.

After checking these rules, Choose among First Match Rule, Best Match Rule or All Match Rule and click on save rule button below.

Now your Rules are active and if anyone pay through the payment method you have selected the discount is applied.
The Discount can be seen on the checkout page.

Now whenever you want to disable this discount rule, you don’t have to delete it, just go to Setting Tab and uncheck this rule.