OOooh, I didn't know that one!
The one I know goes
1 for sorrow, 2 for mirth
3 for a funeral, 4 for a birth
5 for feasting, 6 for work
7 is a duty you daren't shirk
8 for illness, 9 for health
10 means soon you come into wealth (although one of my aunts would say, "soon you lose all your wealth")
Spoiler
and I had an uncle who would finish up, "eleven and up is a flock; beware. They steal your coins and shit in your hair." But he kept pigeons, so he was kind of cynical about all birds and bird-rhymes/bird-lore.