I think it is easier to deny quests if you can never be mistaken for a hero type. I'm sure it helps to be under five feet tall and only about 95 pounds. Who thinks it's a good idea to ask a tiny elf with no melee weapon to go save the world or fetch something from the den of ogres? This snip from Episode 8 of Buffy's Journal shows how 'quest requests' often go for Buffy:
* * *
"The Emperor sent me," I said simply, "I have the Amulet of Kings."
"Who are you?" Jauffre barked, visibly shaken. "What do you know of the Emperor's Death?" Then he sternly continued, "The Amulet of Kings? I don't believe you. You'd better start explaining right now, young lady!"
Instantly, I disliked this man. I pulled the large red amulet from my pack and dropped it on his desk.
"By the Nine!" exclaimed Jauffre. "This
is the Amulet of Kings!" His wide open eyes shifted from the amulet to me and narrowed sharply, "How did you get this?"
Resenting his interrogation, I wondered if he meant that a simple she-elf from Bravil was not worthy of touching the Amulet of Kings, or perhaps he thought I stole it? Defiantly, I lifted my chin and stated, "The Emperor gave it to me." I then curtly described Uriel Septim's last hours and words.
Jauffre told me the story of Martin, the Emperor's illegitimate son. He said Martin had last been seen living as a priest in Kvatch. Then it came: "You must find Martin!"
I snapped back angrily, "No I mustn't! The only reason I am here is because the Emperor and Baurus asked me to deliver this amulet. Both those men were kind and courteous to me. You are neither of those things. You're the boss of the Blades, so send one of them." I planted my hands on my hips and added, "You're not the boss of me!" With that, I walked straight out the door, mounted Superian and continued to Chorrol.
* * *
Of course, she does sometimes accept quests as she shows in this snip from Episode 116:
* * *
"I was going to try and hire the Fighters Guild," she said, "but Aleron took every septim we had. I have no money at all now, Milady. And no one else to turn to." Her eyes swept the floor as the tears started again. "I-I don't know what to -"
"I will help you, Ursanne," I interrupted.
She looked at me with reddened eyes and tear streaked cheeks. "Mara bless you, Milady."
* * *
Edit: EpicFail: Despite my rambling far afield from topic here, I think you have been given some excellent answers and advice in some of the posts above.