CSX Corp., the big railroad, yesterday reported a 60 percent profit decline in the third quarter because of the general recession and a weakening in the domestic and export coal markets.

Richmond-based CSX said third-quarter profits were $42.3 million ($1.01 a share) compared with $104.8 million ($2.54) a year ago. The railroad's revenues were down from $1.4 billion in the third quarter of 1981 to $1.2 billion in the same period this year.

The company said that, even though the railroad hauled fewer commodities during the third quarter of 1981, CSX reported record profits then because of a booming coal business. A mine workers strike in the second quarter of 1981 forced utilities and industrial companies to eat into their inventories of the fuel. During the third quarter of last year, utilities and industrial companies both here and abroad were rebuilding their stockpiles of the fuel.

In the three months just ended, however, the demand for coal declined both in the domestic and export markets for the first time in two years.

In the first nine months of the year the company earned $160.2 million ($3.84) on revenues of $3.8 billion compared with $229.6 million ($5.38) on revenues of $4 billion during the first nine months of last year.