The skies are turning friendly again for United Airlines.

Thanks in large part to its innovative "half-fare coupon" plan, United officals said this week the airline made substantial progess last month toward a return to normal operations after a strike by the machinists' union shut the nation's largest airline down for 58 days.

"Customer response to the half-fare coupons was sensational," Richard J. Ferris, United's chairman and chief executive officer, said this week.

In the three weeks after the strike's end, United distributed 2.2 million of the coupons, which are good for a 50 percent reduction on a regular coach or first-class fare now through Dec. 15. United expects a redemption rate of about 85 percent.

United said relaxing the advance-purchase requirements for promotional fares and a new, low New York-to-California fare also helped.

Although historically it has taken airline four to six months to recover from lengthy work stoppages, Ferris said united expects to shorten that period by as much as half.

Ferris said United's June 1979 traffic was just 12.2 percent less than its June 1978, but he cautioned that meaningful comparisons are difficult because of distortions in both years. In June 1978, United's traffic was inflated because of a strike against Northwest Airlines; this year, besides its efforts to regain traffic lost during its own strike, the airline also was affected by the grounding of its 37 DC10s.

By increasing the flying time of other planes after the grounding, however, United was able to schedule just 11 percent less capacity than it offered last June, he said.

Despite the two-month strike, a United spokesman said United filled 64.6 percent of its available seats during the first six months of the year, up two points from the same period of 1978. In the past three weeks, the airline's load factor has been just below 80 percent, he said.