Let's start with this article from The New York Times of Sept. 19, 1884:
The gossips of South Oyster Bay and Smithville South, Long Island, are busy discussing the alleged marriage of Conklin Vandewater and Miss Cornelia Mann. Mr. Vandewater, who is 19 years of age, is the son of the late Conklin Vandewater, and when he attains his majority will become the possessor of a moderate fortune. For the past year he has been employed as bookkeeper in a wholesale coal yard in Brooklyn, paying occasional visits to South Oyster Bay to see his mother, who resides a short distance from the village. The villagers noticed that when he went to see his mother he was very attentive to Miss Mann, who always happened to be at the railroad station when young Vandewater alighted from the train. He usually accompanied her home, and, it is said, always kissed her "good-bye" at the gate.The 1900 census reveals that "Conkey" and Cornelia had indeed been joined in marriage.
Vandewater was in the village on Sunday, and, in company with other young men, imbibed somewhat freely of Oyster Bay whisky. He left his companions in the evening and called on Miss Mann. He had no recollection of what occurred after, but when he awoke on Monday morning he found the fair Cornelia beside him. He was surprised and asked for an explanation.
"Why, Conkey dear, don't you know that we were married last evening?" and, putting her arms around his neck, she kissed him repeatedly.
Vandewater thought she was joking, but when she exhibited a marriage certificate he thought the thing was getting serious. He left the house and returned to his mother. He stoutly denies that he was married, and says if he was that he must have been drugged. When he left the residence of his alleged wife her mother, Mrs. Mary Jane Mann, followed him and informed his mother of what had occurred. Mrs. Vandewater was thunderstruck and ordered Mrs. Mann out of the house. Mrs. Mann went away, threatening to have Vandewater arrested for abandonment. She has not put her threat in execution.
Miss Mann is a handsome brunette, 17 years of age, and said to a reporter yesterday: "On Sunday Mr. Vandewater, who has been paying attention to me, came to our house and asked me to marry him. I objected at first, but he was so persistent that I finally consented, and we went and got married. That is all there is about it. I know that Conkey loves me, and but for his mother he would be living with me now. But I know he'll come back." The young woman declined to say by whom they had been married. Mr. Vandewater was not at home when the reporter called, and his mother positively refused to speak about the matter. She intimated, however, that if they had been married her son would commence divorce proceedings at once. The villagers are about equally divided for and against the marriage story. A strange feature of the marriage certificate is that Miss Mann will not allow anybody to examine it, nor can she be induced to disclose the name of the clergyman. [Link (pdf)]
Who performed the ceremony?