In a further sign of its renewed vigor, Comnet Corp. last week said it has appointed a former business development director for Firestone Tire & Rubber Co. to a new position managing finances and evaluating new business opportunities for the Washington-based computer services firm.

Joseph R. Sullivan, 41, was tapped for the newly created post of vice president and chief financial officer by Robert S. Bowen, Comnet's president and chief executive officer. Bowen was Sullivan's boss at Firestone and, earlier, at Zenith Electronics Corp.

"Sullivan is one of the ablest executives I have ever come across in the areas of financial analysis and strategic planning," said Bowen, who was recruited from Firestone in the summer of 1984 to reverse the company's dismal performance.

The appointment is another indication that the publicly owned company may have seen the last of two years of losses and disappointing sales -- a period in which a group of dissident stockholders wrested control of the firm and installed the company's current managment. Although Comnet reported a loss of $468,000 on sales of $22.8 million for the fiscal year ending March 31, it has earned a profit in the past three quarters and expects to announce today a profit for its second quarter of fiscal 1986, a spokesman said.

"The company has ended its period of unprofitability," Bowen said. Bowen and Sullivan attribute the turnaround to aggressive marketing of its original line of business, remote computing services and, more specifically, to the award of a $24 million contract with the General Services Administration that will begin in the third quarter.

They also cited as reasons for the improved earnings several new products in its computer software/computer mail division, including a word processing program for IBM mainframe computers, and growth at Ford Laboratories, a New Jersey-based maker of vitamins and nutritional supplements it acquired last year for $11 million.

In an interview, Sullivan said the company will evaluate acquisitions that would "enhance existing divisions," while noting that the laser-printer software and database management segment is expanding and will be moving into new offices in Herndon. But Sullivan would not be more specific and did not rule out efforts to diversify the company's business.