Hannah Hayes, a Mandarin teacher from Reading in the UK has extensively used songs in the teaching of Chinese to introduce fun into the process of learning by repetition and, through the use of music and rhythm. She has written about how she has effectively introduced songs to her teenage students and build up a database of songs and a platform on which to use them.
The 2nd link also has examples of current Chinese music of different genres. Children, even as young as primary age like comparing ‘their’ music to music that Chinese children typically listen to.
'Two tigers' and 'Zhu Ni Shenri Kuaile' are certainly old favourites of teachers but why not learn some modern music too - what about S.H.E's 'Superstar!?' The link even has the lyrics of songs and even though many of the YouTube video clips are now not working, sound files can still be downloaded.