When it come to real traditional songs authors and composers are rarely known. As far as popular songs go the earliest woman author that I know of is Aphra Behn (in London) in the 1680's. I don't know of any women composers of the 17th century. There were women songwriters and composers in the 18th century, but most are not well known. Look through composers names in BUCEM. Woman wrote songs for some opera/musicals also.Best known are Scots women. Add to composers a Lucy Johnson of Hilton as a composer of strathspeys in Scotland, well respected, but died soon after she got married. All three songs know as "The Flowers of the forest" were by 18th century Scots women. Mrs. Hunter (nee Ann Home) also wrote many others including 'Alknomook' (traditional American versions noted in Scarces Songs 1 on my website). Lady Wardlaw wrote "Hardyknute". Later (19th century) we have Mrs. Jordon and Lady John Scott revising older songs to make new popular versions. Anne Julia Hatton seems to have composed the songs for "Tammany', 1794 (but not 'Alknomook' as is claimed). Rosina Emmet seems to have revised a broadside copy to form "Pretty Peggy', 1880, which is traditional as "Marching to Fernario/Fenario" (Scarce Songs 1 on my wesite).
Women authored som songs and composed