"I listen to songs every day."
The 我 should be allowed to come after 每天。Time and subject are interchangable. Usually the longer word comes first.
Then that means either way, the sentence is still the same. The convention doesn't matter whichever way the subject is placed.
I think 我每天听音乐 would mean "I listen to music every day," and 我每天听歌 would mean "I listen to songs every day."