It's hard to really articulate what the parameters are that make one song parody-able and another song not, but if I can come up with a good enough idea for it, I go for it, and if not, then I have to move on.
I write and write and write, and then I edit it down to the parts that I think are amusing, or that help the storyline, or I'll write a notebook full of ideas of anecdotes or story points, and then I'll try and arrange them in a way that they would tell a semi-cohesive story.
I start with a comprehensive list of all the recent songs that have been big hits - and then I go down that list and see if I can come up with funny ideas for them. I can always come up with ideas, but not necessarily good ones!
Like, I have had moments, which I think most people have, where you'll be watching TV, and it'll be interrupted by some tragic event, and you'll actually find yourself thinking, 'I don't want to hear about this train being derailed! What happened to 'The Flintstones'?'
That's a big part of my life - doing things that I'm not prepared to do. Doing things that I don't know how to do, and keep doing them until I get good at them. I always try to put myself out of my comfort zone and out of my depth, and hopefully somewhere along the line I'll catch up.
So that's why one of my rules of parody writing is that it's gotta be funny regardless of whether you know the source material. It has to work on its own merit.