It seems that almost any direct male relation to a King will be given the honor of being called Prince.
Easy examples, Joffrey and Tommen are the sons of King Robert
Harder example, Bran and Rickon are the brothers of the "King" in the North.
Holdover example, Doran is ruler of Dorne and were allowed to maintain the Prince titles after they were not conquered by the dragons. We also see again that a brother, Oberyn, is given the title as well.
The same is true for females (for once!). Myrcella is called a Princess as she is the daughter of King Robert. Shireen like wise is called as her father is claiming to be king.
So we can confirm that brothers of a King will be called "Prince". However, we never see Stannis and Renly given this title (before the death of Robert).
Is there any reasoning for this? Did their positions as Lords of Dragonstone and Storms End and as members of the Small Council somehow "out rank" their status as princes?