I'm Irish living in England and, unfortunately, the only songs I know that sound remotely like a lullaby are Irish rebel songs! It's fine at the mo cos he doesn't understand them but I wanna get out of the habit before he starts asking questions! Problem is, when I sing other stuff he doesn't like it and starts whinging. He's completely fascinated by the fields of athenry and if I sing anything less than all three verses and choruses he whinges! He just goes into a trance with them! I need to have a few other back up songs in my head 
Sorry, I know this is an odd one lol.