To accomplish this via the Net, you need MIDI's (or abc's) lyrics, chords and a music program. Getting an hours worth of music might take a very long time. Are you ready to cope with all that? If not, go to your public library. Take some dimes. Also take the suggestions that Mudcatters have provided so far.

In an encyclopedia, look up the dates for Elizabeth I.

In the 784's (I think that's the number) look for songs from those dates. Copy them right there.

Suggestion: just for laughs, sing a modern song and tell the people it is indeed Elizabethan - just from the time of Elizabeth II.