Doing it with the API is pretty much the same as doing it through a button. By default, PayPal is going to bill the same amount. This is the most common type of recurring payment, and also PayPal only has the fixed amount specified during the creation of the recurring payment.
PayPal can be very convenient, but it's not magic. If you want to bill a different amount this month from the previous, you need to tell PayPal what you want the new amount to be. You can do this either manually through the admin panel, but you can also do it via the API. But you still need to tell PayPal what to change the amount to.
So use the API call that Anagio linked to to create the recurring payment profile (after you've created the billing agreement), and then when you need to alter the billing amount, use the
UpdateRecurringPaymentsProfile API to set the new amount.