The second CONYNGHAM, DD 371, was a destroyer launched 14 September 1934 by Boston Navy Yard, sponsored by Mrs. A. C. G. Johnson and commissioned 4 November 1936, Commander G. C. Hoover in command.

In the spring of 1937, CONYNGHAM made her maiden cruise to ports of northern Europe, and after overhaul at Boston, sailed for San Diego where from 22 October she conducted training exercises. Operations along the west coast, in the Hawaiian Islands and in the Caribbean continued until 2 April 1940, when she sailed from San Diego for Pearl Harbor, and duty with the security patrol. In March 1941, she sailed on a cruise to Samoa Fiji, and Australia, returning to local operations from Pearl Harbor.

On 7 December 1941, when the Japanese attacked Pearl Harbor, CONYNGHAM joined in shooting down several planes, and by 1700 was underway for patrol. She continued to patrol from Pearl Harbor through December, and after a brief overhaul at Mare Island, had escort duty between the west coast and the New Hebrides. With all available forces organized for action as the Japanese threatened Midway in June 1942, CONYNGHAM's escort duties were interrupted to screen carriers in the Battle of Midway, the turning point of the war, fought on 4, 5, and 6 June. In this decisive victory the Japanese were crippled by the loss of four carriers and their best trained and most experienced aviators, a loss from which they never fully recovered. CONYNGHAM returned to escort duties until 16 October 1942, when she put out from Pearl Harbor to screen Enterprise (CV-6) for action in the Southwest Pacific. She defended the carriers in the Battle of the Santa Cruz Islands 26 October, as the American task force encountered heavy air opposition in its turning back of a larger Japanese force bound for Guadalcanal. On 2 November, CONYNGHAM bombarded Kokumbona, and while maneuvering in close quarters, collided with another destroyer. The resulting damage was repaired at Noumea and Pearl Harbor, and she returned to Espiritu Santo 4 February 1943 to resume her support of the Guadalcanal operation. On 7 February she bombarded Doma Cove, and for the next 5 months, continued patrol and escort duties between bases in the South Pacific and Australia.

CONYNGHAM brought gunfire support to landings on Woodlark and Kiriwini Islands off New Guinea from 1 to 3 July 1943, and on 23 August bombarded Finsehhafen, New Guinea. On 4 September she screened landings at Lae, New Guinea, and later that day was attacked by three enemy bombers, which damaged her with their near misses, wounding one of her men. Quickly repaired, she returned to Finsehhafen 22 September to cover landings, then sailed to Brisbane, Australia, for a brief overhaul. She was back in action for the landings on Arawe, New Britain, on 15 December, on Cape Gloucester 26 December, and on Saidor, New Guinea, 2 January 1944. She continued escort and patrol duties in the New Guinea area, aside from a repair period in Australia in January 1944, until she sailed in March for an overhaul at San Francisco.

Returning to Majuro late in May 1944, CONYNGHAM sailed with TF 58, screening battleships during the Marianas operation. On 13 June she fired in the bombardment of Saipan, and remained in the Marianas offering fire support, escort, and patrol services until August. After escorting ships and moving men and supplies among Pacific bases in preparation for the return to the Philippines, CONYNGHAM arrived in Leyte Gulf 4 November screening reinforcements. Taking up patrol there, she was strafed by an enemy float plane on 16 November, which wounded 17 of her men and caused slight damage to the ship. On 7 December she covered the landings in Ormoc Bay under heavy air attack, and on 11 December, entered Ormoc Bay again with reinforcements.

Putting into Manus for replenishment 23 December 1944, CONYNGHAM sailed on to Hollandia to join the screen of a convoy bound for Leyte and on the landings in Lingayen Gulf. Here she joined in pre assault bombardment, and remained on patrol after the landings of 9 January 1945 until 18 January. Her bombardment and fire support effectively contributed to successful landings on Luzon, Mindanao, Palawan, and Borneo through early July. At Subic Bay from 22 July for overhaul, she remained there at the close of the war, and was decommissioned 20 December 1946. Used in the 1946 atomic weapons tests at Bikini, she was destroyed by sinking 2 July 1948.