The assertion of two quotations in the play from the ballad looks to be erroneous. In his edition of 1908, H. S. Murch avers that the reference identified by the play's 1778 editors is "from a different ballad, now lost." Of course, with no full contemporaneous text to compare, we can't be sure.
The doubtful lines are: "You are no loue for me Margret,/ I am no loue for you."
The play was first performed in 1607 or '08. It was published by Walter Burre in 1613. The safest dating for the ballad stanza is thus "1607-1613."
By the way, the play is now believed "quite certainly" to have been written by Francis Beaumont alone.