Solution 1:

The comma is the only acceptable punctuation to place after the valediction:

Sincerely,
John Doe

This is because the period is only necessary at the end of a sentence or abbreviation. The comma, on the other hand, usually separates related phrases within a sentence. In this case, the context is not a sentence (Sincerely, John Doe), but convention has established the usage of a comma in a letter's closing in much the same capacity as in a sentence.