Their Eyes Were Watching God recounts the story of Janie and her life's journey with three different men. The first, Logan, is the man she married because her grandmother was afraid. She was afraid Janie would end up unmarried and pregnant, like Janie's mother; and she was afraid Janie would not be properly taken care of if something happened to her--which, of course, it did. Grandmother wanted her to marry someone decent, so she picked Logan Killicks.
This marriage to Logan was a loveless one, and the time it lasted was generally unhappy for Janie. We don't have a lot of time clues, but we do know a couple of things. Janie and her grandmother have their discussion about marrying Logan in the spring. The next clue is
in the few days to live before she went to Logan Killicks,
so we presume it's still spring. The next time reference is when Janie feels like she should have "felt" in love by now, since
the new moon had been up and down three times.
This gets us to the end of summer, then, probably. Then this line at the end of chapter 3:
So Janie waited a bloom time, and a green time and an orange time. But when the pollen again gilded the sun and sifted down on the world she began to stand around the gate and expect things.
This appears to be summer. The only real unknown is the courting time with Joe, which couldn't have been very long. By these clues, I'm guessing the marriage lasted a year and a season, probably fifteen or sixteen months.