"Zaman zaman yumurta yerim."
Translation:I eat eggs from time to time.
I think "once in a while" is "ara sıra" so "time to time/zaman zaman" is correct. They both indicate something done sporadically , so the meanings are close but not in direct translation.
"Zaman, zaman yumurta yerim." Translation: I eat eggs from time to time.
I have inserted a comma after Zaman, zaman as microsoft word tried to delete the repeated word as a grammatical error.