The music of John Dowland is period. He could never get an official court appointment because he was Catholic.
Others
Thomas Campion
Thomas Morley
John Bartlet
Francis Cutting
Anthony Holborne
Also check "Popular Music of the Olden Time" by William Chappell

remember some of the stuff was really scandalous
WE once did a high school program and did some catches- it was funny watching the kids finally "get" the lyrics!
Have fun-
Julia