Well, Goldcrest beat me to the punch with "Sixteen Guns."
That one seemed like an obvious topic/title for a 16 Tons parody.

Here are some others.   (If no one else has 'em or writes 'em, maybe I'll take a stab at 'em later on.)

"Sixteen Sons"   -- For people whose birth control is absent of ineffective.   (I know "36 Sons" was posted earlier, but "16 Sons" seems like a better parody title.)

"Sixteen Puns" -- Some of our resident Mudcatters should be good at this one.

"Sixteen Buns" -- The saga of 8 nudists sunbathing?

"Sixteen Nuns" -- The fantasy life of a monk?

"Sixteen Huns" -- The nightmare of Attila's victim villagers?

"Sixteen Stuns" -- A song about police brutality with tasers?

Oh, well, y'all can finish the alphabet and come up with others. ;-D