My best guess is that Cornay’s Bridge is located at or nearby Fort Bisland.

McWaters was killed on 14 Jan. 1863 near Cornay's Bridge in St. Mary Parish, while protecting the cotton clad gunboat, Cotton.
http://history-sites.com/cgi-bin/bbs62x/lacwmb/webbbs_config.pl?md=read;id=14470

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January 14, 1863: Battle of Bayou Teche (Corney’s Bridge_, Louisiana – Gen. Godfrey Weitzel, in a campaign to gain Federal control over the winding bayou country, proceeds up this waterway with a flotilla of gunboats under Commodore A.J. Buchanan—the Calhoun, Kinsman, Diana, and Estrella. The gunboats encounter formidable obstructions placed by the Rebels, including torpedoes, near this bridge. The Confederate ironclad steamer, the J.A. Cotton, comes steaming down to meet the Yankees. A lively artillery duel between the Federal ships and the Cotton and Rebel land batteries heats up. After doing battle with the Union gunboats and with land batteries, the Cotton retires back upstream. She reappears twice more, but the effect of Federal fire has damaged her badly. Meanwhile, the Union infantry attack the Rebel positions and finally prevail. The J.A. Cotton ends up destroyed.
http://civilwarsesquicentdaily-wolfshield.blogspot.com/2013/01/january-14-1863-battle-of-bayou-teche.html

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Wreck of the Confederate Gunboat Cotton - Bayou Teche burned by the Rebels January 14th 1863."
Verso: "The Ruins of the 'Cotton' lie across the Bayou Teche about 16 miles above Bewick [sic] City. The morning after the fight of 13th Jan.63 the 'rebs' finding they could not escape with the 'Cotton' ran ashore and set her on fire
http://idesweb.bc.edu/becker/details?pid=25038&jpg2=25020&label=Wreck+of+the+Confederate+Gunboat+Cotton+-+Bayou+Teche,+Louisiana

This would place her wreck just above Fort Bisland

See also:

The Second Battle of Cornay’s Bridge, January 14, 1862 [1863]
http://www.youngsanders.org/youngsandersusscolkinsman.html