You could always buy 2 gift cards, one with each payment method, the gift card are digital in nature and should be available right away. Sometimes the if a gift card is over $50 you have to contact customer service to activate it and buds is closed today.
You could also finance the item through Credova then just pay it off using however many payment methods you want.
More info on Credova here
budsgunshop.com/credova_financing.php

You could do a layaway, pay half on one card, pay the rest with the other card. That's the only way I know how to do it without contacting customer service.

Bryan, You can call Bud’s during business hours at 859-368-0371, or use the blue chat now icon on the right hand side of the screen during those same hours 9am-9pm eastern Mon-Sat and 11-7 Sunday.

Bryan, Buds Customer Service will need to assist with split payments between cards at 1-859-368-0371 9am-9pm EST Mon-Fri. or use the Blue Chat now button at the bottom right corner 9am to 9pm Mon - Sat and 9am to 7pm Sunday.