Mariah Carey makes about 2.7m each year from her Christmas song (sixty million over the first 22 years).
The other way to get rich quick by writing a song is to have it used on a hit TV show, and negotiate to maintain the rights (good luck on that one nowadays). A different Portnoy was set for life after writing Where Everybody Knows Your Name. Every time Cheers airs somewhere, anywhere, he gets a few cents.