Jambo! (Hello)
Habari gani. (How are you)
Mzuri sana. (very fine!)
Hakuna Matata! (No worries/No problem)
And a link to a song:
http://mwanasimba.online.fr/E_songs_jambo.htm
You will find more information about language in there.
I would be interested in learning swahili as well. Anyone helping?