I've tried a long list of variant spellings for Jennison and have tried another long list of wildcard searches. Sometimes these wildcard searches have yielded results (Pealy Gemison in one census, for example).
The other day I found several Jennisons listed in Western New York Land Transactions, including Peter and Rufus. The dates may be a little early to be Rufus Jr. and the Peter could be either Peter Sr. or Peter Jr. There are also transactions for Luther, Oliver and Levi Jennison. Haven't had time to go through the land information in any detail.
Does the obit for Rufus give any information about his siblings? One of the possibilities I've considered is that Purley was the son of one of the older sons of Peter, Sr. and Mehitible. Purley was born 1789 and Mehitible would have been around 40 at that time.
If we could pin down where Dolly was born it might provide a clue to the birthplace of the other three I can't find in the Tan Books.