I found a weird workaround for this. I'm in the same boat. I use prepaid cards because the fewer places my credit card info is stored the better.
I suppose there is supposed to be an Ad for this on the dashboard? I don't have a credit card on my Xbox account, so I can't really get this stuff for free online. I wish MS would already allow that option since they let you do it for Xbox One games, why not avatars? sigh.
Use the mobile Xbox app. (I used Windows Phone so YMMV on iOS or Android.) Go into the avatar marketplace. Both items are listed in the most popular section. You can buy them there with no fuss. The app is a little outdated because it still lists stuff with MS points.