While not the most common, 2 oz is a popular travel size and a good option for trying...
truth be told, "2 oz" in "2 oz bottle of cologne" refers to fluid ounces, unit of volume. In the United States, fluid ounces are commonly used to measure liquids. Knowing the size in ounces is crucial for understanding how much cologne you're getting and how long it might last. (well, almost)
Yes, 2 oz (60 ml) bottles are allowed in carry-on luggage according to TSA guidelines. However, make sure the bottle fits in a quart-sized bag.