I very seriously doubt anyone can give you a time. Remember,at that time where Lincoln was born (then it was Hardin County, Kentucky while today his birth place is now in LaRue County, Kentucky) would have been the frontieer. And in the backwoods of the frontier at that. Time of birth wouldn't have been recorded, even by a doctor. And Lincoln was probably delivered by a midwife. Just like rural doctors at that time midwives would have been unlikely to record time. Best anyone would have gotten was time of day (ie night, morning, noon, midday, ect.). And his birth would not have been recorded right away, that would have been days or even weeks later.