After a man has been found guilty for murder and put on death row, his friend attempts to uncover who’s set him up before time runs out.

If the MC is in fact the friend then give him a much stronger connection to the man on death row. Could he be his brother, twin brother, only matching kidney downer, lover, etc...

The stronger the connection with the man dying the higher the stakes and more compelling a story. Good basic premise though it just needs clarification on who the story is about and the stakes at hand.

Hope this helps.

Because of how short a logline is, it's important to write it from the prospective of lead character.
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"After his best friend is sent to death row, a scrappy newspaper reporter has one week to discover the true killer before his childhood friend is executed."
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One minor thing, The court wouldn't sentence someone acquitted of murder to death row. So telling us he was found guilty of murder isn't needed in the logline, just that he's on death row.