Since I'm no fashionista, I turned to websites such as Family Chronicle, which also has published two books on dating photos, for help in matching styles with a particular era. Consulting experts such as Maureen Taylor, whose website includes a blog and provides teleseminars, are also a good resource.
In my photo, both men are wearing loose-fitting jackets with wide lapels. The elder man is wearing a collarless shirt — too bad, because it's easier to date men's collars and neckties. The younger man is not wearing a necktie, but his shirt has a pointed, flat collar. The jackets seem to indicate a photo taken in the 1870s, but I'm still not certain.
This is the time to turn to common sense. I knew from my earlier research that all three of my great-grandfather's brothers eventually wound up farming in Kansas, after stops in Washington, D.C., and St. Louis. The tintype was taken in front of a painted background — hardly unusual for tintypes, but more likely found in St. Louis than a small town in Kansas that wasn't organized until 1871. In the early 1870s, Michael would have been in his twenties and Peter in his teens and both were living in St. Louis. Timothy would have been too young to be either brother.
Therefore the photo is more than likely Michael and Peter, perhaps taken before Peter left for Kansas to live with relatives, leaving Michael behind. Sometimes a good guess is as close as you'll get to the answers.