The Justice Department unit set up to prosecute American Corporations that make payoffs to foreign officials won its first court victory here yesterday: a guilty plea by the New York firm that distributes the postage stamps of Cook Islands, a tiny country 1,8000 miles off the coast of New Zealand.

Kenny International Inc. and its director, Finbar B. Kenny, entered the plea and were immediately fined a total of $50,000 in connection with their interference with the 1978 Cook Islands elections.

Kenny also agreed yesterday to plead guilty in the Cook Islands in connection with the scandal that has grown out of the election, and to testify against the island's former prime minister.

The prime minister was ousted from office after diverting $337,00 in the country's stamp income to charter six jets to fly his supporters to the polls from New Zealand to vote for him.

The case was centered around the Cook Islands' single largest source of revenue, the money it gets from collectors for stamps promoted and distributed around the world by Kenny and his firm.

Kenny, an american who has headed the Cook Islands government philatelic department since 1965, is the sole distributor of the stamps, and keeps 50 percent of what he sells outside the islands. In 1978, his stamp sales totaled $1.5 million, and the Cook Islands' share of that amounted to 20 percent of its total revenues.

Acording to the Justice Department's evidence filed in court yesterday, the island's premier, Sir Albert Henry, scheduled a general election in 1978. The stamp contract would have come up for renewal during the next premier's term of office, and Kenny could be assured of keeping the contract only if Henry remained in office, the Justice Department said.

Henry, in turn, is said to have figured the only way to assure his election was to fly his Cook Islands Party supporters from New Zealand to the islands to vote. As many Cook Islanders live in New Zealand as on the country's islands, and through they may vote, no provisions are made for absentee ballots, the Justice Department said.

Henry then sent a personal representative to Hawaii to solicit funds from Kenny to fly the Cook Islanders to their voting places, the evidence continued, an illegal act under cook Islands law.

Kenny agreed, the Justice Department said, but only if the transaction remained secret. He even devised a code to hide the transactions in Telex messages, and set up shell corporations to hide the money exchange. He met with Henry in Hawaii to make final arrangements for the six Boeing 737s.

The final payment was made in New Zealand currency, listed in court papers as "nz337,000 (having an approximate equivalent value in United States dollars)."

Henry won the election in March, 1978, but was thrown out of office in July 1978, in proceedings contesting the election by his opponent, Dr. Thomas Davis. The islands' chief justice ousted Henry after disallowing the votes of the Cook Islands Party supporters whose travel had been subsidized as "unlawful votes tainted by bribery."

Attorneys for Kenny said the plea was a technical violation of the Foreign Currupt Practices Act of 1977, and noted that the current Cook Islands premier "it urging" that Kenny continue to run the country's philatelic bureau.

Attorney Sheldon H. Elsen said Denny received no Personal Benefit from the transaction, and that the funds he paid represented an expedited payment legitimately due to the country.

"It would have been extremely difficult for the company or any other servant of a foreign government not to comply with a request from the head of that government for advance payment of funds to which it is rightfully entitled, or to control the use of those funds subsequent to transfer, no matter what his suspicions," Elsen said.

Cook Islands has full independence internal affairs, but depends on New Zealand for security and foreign policy. The islands are named after navigator James Cook, who visted them in the 1770s, and have 18,000 citizens.

The stamp company could have Been fined up to $1 million under the U.S. law.