The article was in the Wilmington notes section of the Chester Times (Delaware County, PA.) Newspaper, dated April 30, 1937. It listed key members of the church who were involved in a convention. No other Carsins were listed. Perhaps Webster was buried in that church's cemetery?
I'm sure you're aware that the Carsins family came from Harford County, MD., and appear on Rootsweb.com (World Connect)?
Webster S. Carsins completed a WWII draft registration card in 1942. So obviously, he lived beyond that date.
He doesn't appear to be in the Social Security Death Index, so you might assume that he died before 1960.
That's a death window of 1942-1960.
The University of Delaware Library has the best collection of Delaware newspapers on microfilm, so once you find his date of death, you might want to look up his obit there.
The state of Delaware kept excellent death records, and his death certificate should be on file. The Delaware Public Archives should be able to help.
Here's a photo his parent's and sister's grave marker: