Jean, I found a few things for the Greenaways which may be of help to you; I'm not related, just a volunteer: 1870 Will County, ILReid Twp.Braidwood P.O.page 435 5 August #446#502 Greenaway, Samuelage 32butcherb. England Mary26England Celia3Illinois Susan1/12Illinois b. April Strickland, Ann16 domestic serv.Ireland Susan is shown as having been born in April, but only 1 month old in August.
On the 1880 census of Lake Twp., Cook County, IL, the daughter who was 2 years old was ALMA, not ANNA. They also had Susan and Celia [Cellelia]. You already had this census data.
From the Illinois Marriage Index: Greenaway, Celia A.to Fred J. Kievlan[both residents of Cook County] married 1-1-1889 in McHenry County
McHenry County, Illinois CemeteriesVol. IISouthwest Townshipspage 89Oakland CemeteryWoodstock, ILDorr Twp. Greenaway, Mary W.2-9-1844 - 10-26-1884 Greenaway, Lulu J.daughter of Sam and Maryaged 3 yrs./7 months/2 days Greenaway, Elizabeth W. daughter of Sam and Maryaged 9 days Greenaway, Mary W.daughter of Sam and Maryaged 1 month/7 days Greenaway, unknownburied ca 3-1-1905[see below death information; this is Samuel's grave] Edwards, Williamfather2-28-1810 - 10-10-1896
There were no dates given for any of the Greenway daughters in the cemetery book, just ages.
Illinois Death Index Pre 1916 Greenaway, Samuel J.d. 3-5-1905aged 67 years certificate # 00005431Cook County I'm not sure if Cook County was recording the names of parents on death certificates pre 1916, or not.
After finding that William Edwards was the father of Mary, I checked the IGI at FamilySearch to see if I could find anyone who might match her:
Mary Waldron Edwardschristened 8 April 1844Bridport, Dorset, Englandfather: William Edwardsmother: Ann
William Edwards married to Ann Waldron25 December 1830 Burton Bradstock, Dorset, England
Your Mary's middle initial of "W" seems to be quite unusual. This was the only Mary W. in the IGI; although there were tons of Mary Anns and Mary Janes. Notice that the above daughters were given a middle initial of "W" also, except for Lulu J.Maybe for the maiden name of Mary's mother? [maybe Ann Waldron?]
I live on the border of McHenry County and Kane County. The Woodstock library has newspapers on microfilm; if you contact them and give death dates, it is possible that obits could be found which might give more information.