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It's completely random.
Didn't know its rare i guess ill just keep my two cows
If the game tries to have an animal give birth, it selects an upgraded barn (so at least to the level where you can have goats) that isn't full and rolls another 0.55% chance to continue with the birth-giving process, multiplied by the amount of animals inside the barn. If this check fails, the next upgraded, not full barn gets the same check, until you run out of barns to check at which point the event does not fire. If the check passes, a random animal in the barn is chosen. If the animal is a baby, or if pregnancy is not enabled, the event will not fire. If it is an adult with pregnancy enabled, the animal will give birth during the night.
So essentially you have a 0.275% chance each night, per barn animal, to see a birth, under the assumption you don't have any baby animals or disallowed pregnancy for any of them. For just the two cows, it'd take ~91 days (just over three seasons) just to hit the 50% mark over time.
Gonna save up to upgrade my barn