(Not a teacher)
If it's the name of the song, then the band can call it whatever they like really, with no regards to grammatical correctness.
'Night' and 'Nightly' can both be adjectives that mean 'of/like the night'. 'Nightly' also has the meaning of 'occuring each night'.
A 'nightly song' would be a song that is performed each night.
- For Teachers