They were willing to lobby for a 7.5 cent coin and update their machines to recognize that, so it sounds like they could have handled dimes. The reason they didn't want to switch to dimes is that it was too big of a price jump.
I'm curious how they eventually handled the changeover. I seem to vaguely recall Cokes when they were a dime (in the mid-sixties or thereabouts) in the machine. I also don't ever recall vending machines taking pennies or giving change in pennies--though perhaps they did. I just also have some trouble believing that Coke vending machines pretty much doubled in price over a few years.
I don't think vending machines even now will give pennies in change.