When you mentioned the name COAKLEY, I recalled that I had come across it in my research. I have a copy of the 1860 Christiansted census for 24 Kings Cross (property owned by Anthony GARNIER), which has an Eliza COAKLEY, age 50, living there. She was Episcopal, unmarried, and worked as a Washer. I wonder if this was the Eliza WOODS you mentioned. If she was his third wife, it may not have been a legal marriage but perhaps she used his name. The ages are not too far off from each other - she could have been a little bit younger than he.
Eliza COAKLEY lived there with a Margarett IVERSEN/JENSEN (hard to read surname), age 45, Lutheran, unmarried, washer. Several other individuals lived in the same household, and were much younger: Mary ISAAC, age 22, Episcopal, Married, a peddler; Rebecca COOPER, age 19, Episcopal, Unmarried, a houseservant; Susana COOPER, age 14, Episcopal, Unmarried, a house servant; Jens ERICKSEN, age 7, Lutheran; Carl ERICKSEN, age 4, Lutheran; Arek ERICKSEN, age 1 1/2, Lutheran.
I have a Jens ERICKSEN in my family and this one is at about the right age (his daughter Wilhelmina ERICKSEN was born in 1876, which would make this Jens 23 at the time of her birth). I've never been able to establish whether or not the Jens ERICKSEN in the 1860 census is my ancestor or not. This household had such a mix of surnames, I can't figure it out. It is clearly one household, but who knows if they were all related to each other. I wonder if you've heard any of these surnames mentioned in connection with your COAKLEYs.
Anyone with some feedback regarding the data in this particular census entry, please share your thoughts! By the way, the census taker's name was A. M. MONSANTO.