I heard back from my cousin and he is very pleased to learn more about the rocking chair! Thank-you everyone! Our great-grandparents were married in June of 1910, so the 1-20-10 date fits very well with the time they would have become engaged and would have been putting together their household. In fact, a piece of my great-grandfather's parent's house was cut off, dragged across the street the street and made into a house for the newlyweds about that same time. Since the chair appears to be older than the inscription, this all makes perfect sense, and it very likely came from my great-great-grandparents, Franklin and Florence Ely.
So that you can see who owned the chair, here they are:
Our great-grandparents, Charlotte Richardson Ely and Joseph Bolles Ely
Our great-great-grandfather Franklin Ely
Our great-great-grandmother Florence Amanda Bradbury Ely