The phrase "son of a brother-in-law" is quite specific, but there are a few synonyms that could potentially be used. One option is "nephew by marriage," which refers to a child of one's spouse's sibling. Another possibility is "cousin-in-law," which could refer to someone who is related to you by marriage rather than blood. "Half-nephew" or "half-cousin" could also be used if the relative in question is only related to you through one parent rather than both. Ultimately, the best synonym to use will depend on the specific context and the relationship between the people involved.