I think I might to add some confusion.I've been looking at the census and finding these people very difficult to track down.Here are some things for you to think about.
There's a Phebe Knowles, age 10, in Broome, Schoharie Co, NY in 1860.She is, unfortunately, in the household of Phebe Knowles, age 64who also has a Frederick, who appears to be her son, and an Asa, age 6.
I don't have an index for the 1850 census so I went page by page through the 54 pages of the census for the town of Broome.The Knowles households were on the last pages so I know that they were the only two Knowles households in the town (at least that were reported on the census).One was Frederick's and the other was for a Runnells Knowles, age 57, born in RI with wife Pheobe, born in CT and a Joseph H. 21 and what appears to be a Julian, 24. "Julian" is a female, though, and the image quality isn't great--it could be Julia or just a mistake.The fact that they are listed out of order for age suggests to me that they may be husband and wife rather than siblings.
So--since you have a death certificate as one source, and those are often reported by people who don't necessarily know the facts, and since there's a son Joseph, is it possible that your Henry B. Knowlton could be Joseph H. Knowles?
I looked for Charles VanBuren and I guess he's the one in the household of George VanBuren in Jefferson, Scoharie, NY in 1870--he's age 18 there.
There was something strange or maybe very sad happening, it looks like.I can't find anyone in 1860 who looks like Phebe's parent.If she were orphaned as a young child it wouldn't be too surprising if by the time she died the facts of her parentage were unclear to the reporter of the death certificate.
If this is the right Phebe, and she is the grandchild of Runnells Knowles, I think this may be a fairly old RI family. I suspect that Runnells is really Reynolds, especially since I learned that a Reynolds Knowles was an early settler of Broome in 1817. The name Reynolds appears in the RI Knowles family, starting with a spousal surname.There's an article on the Henry Knowles family of RI in the NEHG Register if you get to that point.
I wish I had been able to find more--this got more interesting as it got more frustrating.I realize all my guesses are only guesses.I have no idea if the Phebe in the household of the elder Phebe is yours, if she is if she's the grandaughter of Runnells, and if Runnells is really Reynolds and from the line of Henry Knowles of RI, but it all seems possible to likely to me.