If you're looking to playfuly annoy your dad with a song, consider something that's overly cheesy or has a repetitive, catchy chorus. "Baby Shark" is a classic choice that tends to get stuck in people's heads. Another option is "The Song That Never Ends" by Lamb Chop, which, as the name suggests, just goes on and on.
Alternatively, you could parody one of his favorite songs by changing the lyrics to something silly or teasingly annoying. Just keep it light-hearted and fun!