Take the lyrics:
... Now he lives in the islands
Fishing the pilin's (instead of pilings) ...
Is there a word that means to alter the pronunciation to achieve a rhyme (in song)?
In rap music, the term bending words is used when rappers create rhymes where there otherwise wouldn't be a true rhyme.
Here is a YouTube video where the artist Eminem talked with the news program 60 Minutes on this topic.
There may be other names for this rhyming device, too – I'm not claiming this is the right answer. Or, put another way:
The term I've heard used for this sort of fudging is "allowable rhyme" - meaning that it's allowable by a generous interpretation of the rules, but it just ain't right.
H.P. Lovecraft (he of Gothic-horror fame, ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn!) wrote a famous essay on the topic called, appropriately enough, The Allowable Rhyme. He did not approve.