my friend if the chair rail is made from flat stock on the back, then two 45's will make the junction nice and neat if the walls are 90 degree angles.
Your second way will work, but that is usually reserved for crown molding.
I guess my first question is: do you have a mitre box and saw? If yes, then do the 2 each of 45's. If you do not have a mitre box saw and box, then do the coping only if you have a coping saw.
Get some caulk also, because your corners will not be true.
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