What? 2-3k words to get someone to cry, who is *expecting* you to get them to cry? That's a single chapter to introduce a character, get emotionally invested to a sufficient depth, and then kill them in a way that invoke the proper level of tragedy rather than throwing the reader out of the narrative.
I think that the challenge is incredibly flawed; I can't imagine *any* author pulling that off successfully.
Hmm. At least, if you need to kill the target character. That's what is so heavy handed as to throw one out of the narrative.
However, if the challenge is to get her to cry, I do have an option. Don't kill or even hurt the character, physically at least. Make the character cry. Treat the following as a template:
Scenario: PoV character meets target cute character, probably a young-ish girl, there's some bonding, etc. Narrative focus is on the girl a lot, but the girl has a pet dog that she clearly loves, but the dog should get only a small part of the narrative attention.
As you get close to the end of the chapter, something happens. Let's make it an earthquake for this scenario. Girl is in danger, the PoV character reacts and manages to save the girl, maybe getting a little injured in the process. The danger passes, and everyone is starting to relax. Then the girl asks, "Wait, where's Fluffy?" If you do it just right, both the PoV character and the reader's hearts break watching the little girl's heart break as reality sets in and the dog's body is found.
Note: this can be done with a sentimental object or something as well (such as a stuffed animal), so long as you sell the emotional bond and how it break's the girl's heart.