The Coca-Cola Co. yesterday reported income of $139 million ($1.13 a share) from continuing operations in the second quarter, while Continental Airlines said rising revenues helped cut losses.

Coca-Cola's income figures reflected increases of 10.1 percent over last year's second-quarter income and 9.7 percent over the second quarter of 1981's per-share income. Revenue in the second quarter was $1.56 billion on continuing operations, a 2 percent decline from $1.6 billion.

Income from continuing operations for the first half of 1982 was $247.4 million, an increase of 10.2 percent over the prior year. Per-share income for the first half of 1982 was $2, a 9.9 percent increase over the first half of 1981.

At its meeting yesterday, Coke's board of directors declared a regular quarterly dividend of 62 cents a share, payable Oct. 1 to stockholders of record on Sept. 15, 1982.

Continental Airlines reduced its net loss in the second quarter to $4.8 million from $9 million a year ago as revenues rose 7.6 percent.

The operating loss before tax and other credits was cut to $13.9 million from $22 million a year ago. The results also were an improvement over those of the first quarter. Revenues rose to $289.93 million from $269.38 million. The first-half net loss was cut to $27.91 million from $34.71 million a year ago as revenues rose to $566.07 million from $496.69 million.

Chairman Frank Lorenzo said he was encouraged because the improvement occurred in spite of the cost of developing the new second transportation hub at Houston to coordinate Continental's operations and those of Texas International Airlines.

Texas Air Corp., which wholly owns Texas International and controls 67 percent of New York Air and 51 percent of Continental, yesterday announced a preliminary consolidated net loss of $7.9 million ($1.37 a share) in the 1982 second quarter compared with a restated net loss of $4.1 million in the year previous period.

Texas Air said the figure reflects its share of Continental, Texas Air and New York Air losses, and net income of $6.4 million from parent company operations and gains from the sale of certain assets.

For the six months ended June 30, Texas Air reported a consolidated net loss of $38.6 million against a restated net loss of $5.2 million a year earlier.