NEW YORK, DEC. 15 -- The stock market posted some modest gains today, helped by declining interest rates and a brighter inflation outlook.

Analysts said they were impressed by the market's resilience in the face of declines in prices of some major banking stocks and afternoon profit-taking.

On other exchanges, gold prices tumbled and the dollar firmed in response to a sharp drop in oil prices.

The Dow Jones industrial average of 30 stocks, which climbed 65.82 points on Monday after a 100-point rise last week, rose another 8.62 to close at 1941.48.

Advancing issues led decliners by a ratio of about 9 to 7 among stocks listed on the New York Stock Exchange, with 928 stocks up, 688 down and 376 unchanged. Volume on the Big Board came to 214.97 million shares, up from 187.69 million Monday.

Crude oil prices continued to fall in the wake of OPEC's adoption Monday of a new agreement that industry analysts say will do little to diminish the world's oversupply. The price of benchmark West Texas intermediate crude oil dropped 81 cents, to $16.63 a barrel.

Michael Metz, a market analyst for Oppenheimer & Co., said financial markets interpreted the oil price slide as a sign that inflation need not be a worry. As a result, he said, the Federal Reserve will have more flexibility to relax its monetary policy and encourage lower interest rates.

Analysts said inflation worries in the metals and currency markets have been dampened by the oil price drop. At the Republic National Bank of New York, gold bullion was bid at $483.25 a troy ounce at 4 p.m., off $12.25 from Monday's late price.

The dollar got off to a slow start, slipping to a new low of 126.95 yen in Tokyo from 128 yen, despite heavy intervention by the Bank of Japan. Later, in London, the dollar closed slightly higher at 127.40 yen, and in New York it closed at 127.60, down from 127.995 late Monday.

The Reagan administration reiterated today that it is not seeking further declines in the dollar. The statement by White House spokesman Marlin Fitzwater was the same as it was the day before and, he said, "I'll say it tomorrow."

Several major banking company stocks fell in a selloff that analysts said stemmed from concerns that banks with loans to less-developed countries may not get their money back. Bank of Boston Corp. stirred those concerns Monday by announcing it will take a charge of $200 million against such loans.

Citicorp led the NYSE's list of most actively traded stocks, falling 7/8 to 16 5/8. Chemical New York fell 3 1/4 to 20 3/4, Chase Manhattan tumbled 2 1/4 to 20 1/8 and First Chicago fell 1 1/2 to 17.