What do you mean by "Modern Battery"? NAPA, O'Reilly's and most all of the other popular auto stores have the battery you need. Just make sure to read the code which tells the manufacture date. Because these batteries are not in high demand, they sometimes sit on the shelf of a warehouse for months or even more than a year. There is not a lot worse on a battery than sitting on a shelf not being used.
If you mean a gel filled vice acid filled battery, they are available too. Not sure from where, but I know my friend just bought one for a '58 Edsel which takes the same battery as your '56 Ford. Best bet would be to Google it or if you live in a large city, check with a Battery Depot type outlet.