Hi Joyce,
To back to your original question for a minute.

After speaking with the chap at the Rhode Island Archives, he's certain you contacted the Rhode Island Vital Records office which cover the years after 1908 to present date. Before 1908 all vital records are held at the Rhode Island Archives. They are two separate entities.
Rhode Island State Archives
337 Westminister Street
Providence, Rhode Island 02903
401-222-2353
Certified Copy are $2
Photo Copies are 15 cents
Rhode Island General Laws stipulate that all records of birth and marriage are closed for 100 years and Death records are 50 years.
Birth and Marriages 1853-1908 are indexed
Deaths 1853-1958
Prior to 1853 on micro film only. Original manuscripts maintained at the local level.
Copied from the Vital Record Order Form
.................................................................................
Your James Issac Hickman did in fact pass away on 4 June 1931, as Jacquie found on Ancestry. Today I called the archives to inquiry about the missing record. It seems as though it was found in the clerk's film reader the other day, after I left.

The clerk was nice enough to fax me a copy. I'll be scanning them on over tonight.
Appears that James was buried in Canton, Massachusetts. The cemetery name isn't listed on his cert. Maybe he's buried in a family plot in Massachusetts. Why else would they travel to another state to bury him?
I'll let you and Jacquie sort through your census results.
Lexi