A couple sentenced last month on charges related to sex-oriented businesses they own along the District's 14th Street strip won a 29-day delay yesterday in reporting to federal prison.

U.S. District Judge Thomas A. Flannery granted the request by Herbert and Mary Cole after the couple's lawyer said they needed time to settle their business affairs and arrange to pay overdue federal taxes.

Flannery ordered that the couple surrender to the Bureau of Prisons on Jan. 31 instead of Jan. 2.

The Coles were forced to sell their 14th Street property, which houses Casino Royal, a theater featuring adult films, as part of a plea agreement reached earlier this year with federal prosecutors. The couple forfeited $1.5 million from the sale to the Internal Revenue Service to satisfy back taxes for 1977 through 1981.

The building was heavily damaged early Wednesday in a blaze that claimed the life of a D.C. firefighter.

The Coles' lawyer, Roger E. Zuckerman, told Flannery that the Coles still owe back taxes for 1982 and 1983. Zuckerman said the couple's 1984 taxes also have been complicated by the sale of the Casino Royal building, which was bought for about $5 million by a group of developers.

Herbert Cole, 47, was sentenced to two to eight years in prison and fined $10,000 on tax evasion and racketeering charges connected to the sex businesses, which the government alleged were fronts for prostitution.

His wife, Mary, 44, was sentenced to six months to three years in prison and fined $10,000 for tax evasion.

Zuckerman said that the Coles own substantial holdings in Maryland.

Assistant U.S. Attorney Brian M. Murtagh opposed the delay, saying the Coles "have a bad record of paying the IRS and secreting their assets to avoid paying taxes."

Murtagh said Herbert Cole still is a partner in the Random Co., which owns "This Is It?" a topless go-go bar on 14th Street.