After the Civil War began, young Cuney found work on a steamship running between Cincinnati and New Orleans on the Ohio and Mississippi rivers, teaching himself law and literature during the long passages. He settled in Galveston, where in 1870, three thousand Black residents made up nearly a quarter of the city's population of 13,818. Cuney rose quickly. By 1870, he was sergeant-at-arms of the Texas Legislature. He befriended Republican Governor Edmund J. Davis and won appointment as a delegate to the 1872 Republican National Convention, a role he would hold for two decades. He became head of the Galveston Union League, school director for Galveston County, federal customs inspector for the Port of Galveston, and secretary of the Republican State Executive Committee. In 1875, he was elected the first Grand Master of what is now the Most Worshipful Prince Hall Grand Lodge of Texas, contributing to the growth of Black Freemasonry across the state.

Cuney understood that political power without economic power was fragile. White unions controlled the labor market on Galveston's docks, shutting Black workers out of the port's booming trade. Cuney established his own stevedoring business and pushed Black workers to cross white picket lines and accept lower wages to gain a foothold. He recruited additional Black dock workers from New Orleans. The strategy was blunt and controversial, but it worked. The Trades Assembly was gradually forced to reconsider its racial policies and grant concessions. The increased power of unionized Black dock workers eventually led to interracial unions in Galveston during the 1890s and into the early 1900s, a remarkable achievement in the segregated South. Galveston's biracial labor alliances on the waterfront became one of the most striking exceptions to the rigid racial hierarchies that defined the era.

In 1889, Cuney was appointed United States Collector of Customs for the Port of Galveston, the highest-ranking federal appointment held by any African American in the late 19th-century South. The New York Times reported on his accomplishments. He rose to chairman of the Texas Republican Party and became a national committeeman, leveraging the Black vote that he had helped build. His efforts to recruit and register Black voters contributed to more than 100,000 African Americans voting annually in Texas during the 1890s. But Cuney's success provoked backlash. At the 1888 Republican National Convention, a group of conservative whites tried to expel prominent Black leaders from the party. Cuney gave the movement a name that stuck: the Lily-White Movement. He fought it, maintaining control of the Texas Republican Party for a time, but the forces of racial exclusion were gathering strength.

Cuney married Adelina Dowdie, a schoolteacher, on July 5, 1871. She was also mixed race, the daughter of an enslaved mother and a white planter. The couple filled their home with music and art. Cuney played the violin; Adelina was a soprano. They raised their children on Shakespeare and education, working to shelter them from Galveston's pervasive racism while keeping close ties to Cuney's brothers and their families nearby. Their daughter Maud studied at the New England Conservatory of Music in Boston and became an accomplished pianist, musicologist, and author, publishing a biography of her father in 1913. Their son Lloyd Garrison Cuney, named after the abolitionist William Lloyd Garrison, became an official in the Congregational Church.

Cuney died on March 3, 1898, at age 51. Within a decade, the world he had built was being dismantled. Texas instituted poll taxes and white primaries, slashing the number of Black voters from 100,000 in the 1890s to fewer than 5,000 by 1906. The Lily-White Movement he had named consumed the Texas Republican Party by 1912, shutting Black Texans out of politics entirely. It would take the federal civil rights legislation of the 1960s to restore what Cuney had achieved. Yet his legacy endures. Wright Cuney Park in Galveston, between Broadway and Harborside Drive near the wharves where he built his stevedoring empire, hosts the city's annual Juneteenth celebration. The town of Cuney, Texas, was named in his honor. His example inspired generations of Black leaders who followed, proof that even in the most hostile circumstances, political organizing and economic self-determination could shift the ground beneath entrenched power.