I think a few of the themes from "A Poison Tree" are anger, revenge, and deceit. I have a few modern songs that I feel fit a few of those themes.
Carrie Underwood's "Before He Cheats" is a song about revenge. The song focuses on how the narrator vandalizes her cheating boyfriend's truck with a baseball bat. It fits with "A Poison Tree" because her anger resulted in her taking action against another person in a hurtful way, although nobody winds up dead like they do in the poem.
Aerosmith's "Janie's Got a Gun" works with anger, revenge, and deceit. The general gist of the song is that Janie kills her father for sexually abusing her. Obviously the father is being deceitful about what is going on in his own house. The anger and revenge come from Janie who "put a bullet in his brain." So like the poem, it ends in death by murder.
Another option is to pick just about anything by Taylor Swift. She just can't seem to write a song without it being focused on revenge.