Stannis Baratheon turned away from the window, and the ghosts who moved upon the southern sea. “The Seven have never brought me so much as a sparrow. It is time I tried another hawk, Davos. A red hawk.” What do you think is red hawk? Is it related to dragon or another rh'ollo related?
Well. I am pretty sure, the answer is in the text itself:
"I trusted in his wisdom and your wiles, and what did they avail me, smuggler? The storm lords sent you packing. I went to them a beggar and they laughed at me. Well, there will be no more begging, and no more laughing either. The Iron Throne is mine by rights, but how am I to take it? There are four kings in the realm, and three of them have more men and more gold than I do. I have ships . . . and I have her. The red woman. Half my knights are afraid even to say her name, did you know? If she can do nothing else, a sorceress who can inspire such dread in grown men is not to be despised. A frightened man is a beaten man. And perhaps she can do more. I mean to find out.
"When I was a lad I found an injured goshawk and nursed her back to health. Proudwing, I named her. She would perch on my shoulder and flutter from room to room after me and take food from my hand, but she would not soar. Time and again I would take her hawking, but she never flew higher than the treetops. Robert called her Weakwing. He owned a gyrfalcon named Thunderclap who never missed her strike. One day our great-uncle Ser Harbert told me to try a different bird. I was making a fool of myself with Proudwing, he said, and he was right." Stannis Baratheon turned away from the window, and the ghosts who moved upon the southern sea. "The Seven have never brought me so much as a sparrow. It is time I tried another hawk, Davos. A red hawk." (ACOK, Davos I)
Next thing, Stanny proceeds to send a shadow baby to stab his little brother through the throat.
The red hawk is Melisandre and her red god, and her dark dark blood magic.
Considering the sparrows that Stannis laments will become synonymous with a brutal, unrelenting and merciless religious fanaticism later in the books, it's a not-so-subtle suggestion that Stannis is making a big mistake.