The House Public Works Committee decided yesterday to try again to persuade Congress to put up a pile of money to convert the little-used Visitors Center at Union Station back into a railroad station.

More than a decade ago, with then-Rep. Kenneth Gray (D-Ill.) leading the charge, the committee convinced Congress that trains were going out of style and that the station should be turned into a center for tourists. The government spent more than $21 million to partially build a parking garage and create a center that scarcely anyone visits.

Last year the committee asked the House to authorize $39 million more to change the concourse back to a railroad station and run the tracks back in there. The House killed the bill. Now the committee has cut the price tag to an extra $36 million and is sending the bill back to the House floor after Easter. An agrument for it is that the government is committed to paying rent of $3.1 million a year for the station-center for the next 21 years whether or not it uses the facilities.

The committee also approved a bill authorizing $3.5 million to buy a 1 1/2-acre parking lot south of the Rayburn parking garage to block construction of private offices on the site.

Also approved was a bill authorizing construction of a $92 million building for Social Security offices in the Queens section of New York City. This bill has been sought by area congressmen and Sen. Daniel P. Moynihan (D-N.Y.). It came out of committee shortly after Moynihan withdrew his "hold" on Senate action to place a plaque honoring Ralph Becker, a Republican who was paid counsel of the Kennedy Center's board of trustees, in the center's foyer. The Becker measure was sponsored by Rep. William Harsha of Ohio, senior Republican on the House Public Works Committee.