Pennies and the word cents mean almost the same thing, as in I have 4 pennies (the coins) I have 4 cents (the amount of money). The word cents sounds like the word sense, which means basic knowledge or understanding. So in your example, the verse the son read did not make any sense to his mother, so she said she would give him some "cents". Play on words.

Note (a) that the grammar is 'wrong' here. It is deliberately written to sound like the speech of uneducated people, or people that speak in a dialect. (b) the pennies/cents/sense joke/idea only works in American English. British English doesn't use 'cents', and Australasian English doesn't use 'pennies'.