Cosens was born in Southampton, the son of John Cosens, an attorney.
He was vicar of St. Martin's, West Drayton 1760-1765, and minister of Teddington, 1761-1791.
- The Economy of Beauty: In a series of fables; addressed to the ladies. London: J. Wilkie / F. Newbery, 1772.
- Windsor: An ode. Brentford, UK: P. Norbury, for G. Robinson, London, et al, 1778.
- Sermons on Useful and Important Subjects. (2 volumes), London: T. Cadell, J. Deighton, et al,1793.
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