Pushovers of the World, Unite!
I suspect we all have known people like this. I've used HellOnHeels' technique of being vague, and that sometimes works. I'll share another tecnique that can work more directly.
My M. acts hurt, and even cries, at anything and everything that she doesn't like to hear from me. It worked for decades to control me. And internalizing that pattern, of buckling under when somebody acts hurt, made me an easy mark for others.
I have finally learned to stand up to that tactic. I address it by:
1. Acknowledge what the other person has asked of me. ("Lucy, I hear that you'd like me to ________.")
2. State my feelings about the request. ("I notice that I'm feeling: irritated, sad, upset, defensive, angry, doubtful, uncomfortable, shut down…".) Any real feeling.
3. Give my decision as "So, no, that does not work for me." Speak in a calm, friendly voice, and under no circumstances ever attempt to explain further or give any excuses or reasons, and DO NOT APOLOGIZE. Those will only invite wheedling, tears, or argument.
But NOBODY can sanely tell you your own authentic feelings are wrong. You've got a right to your needs, just as your acquaintance has a right to hers.
4. Practice with another friend or family member, or even in a mirror, until this feels natural.
Good luck!