For two hours yesterday, Prince George's County Executive Parris Glendening told jokes, displayed graphs and handed out stacks of budget documents in an effort to solve simultaneously two of his most pressing problems: the county's looming $30 million deficit and his uneasy relations with the county's representatives to the General Assembly.

"It's the Treaty of Parris," joked Del. Timothy Maloney, one of 19 legislators who attended the meeting, and one of Glendening's severest critics. Though all are Democrats, Maloney and other legislators have criticized Glendening in recent weeks for a multitude of political sins, from failing to consult them before announcing that the county faced layoffs of up to 600 public employes, to announcing that he needed more state aid to promoting a solution that they didn't like.

Yesterday, Glendening tried to convince the delegates of the severity of the county's plight and to hear their suggestions, but most of all he held out the olive branch during the meeting at the County Office Building in Upper Marlboro.

"Welcome back to the fifth floor," Glendening began. "For some of you who may never have been here before, let me say . . . it's now more open," he said in a reference to his predecessor, Republican Lawrence J. Hogan.

Glendening repeated his belief that the county faces a deficit ranging from $29 million to $38 million, and layoffs, unless additional sources of revenue are found. He offered what he repeatedly insisted were not "proposals" but rather "examples of possible adjustments."

Glendening suggested that the state lift the ceiling on the amount the county can collect from state income tax, from the currrent 50 percent to either 55 or 60 percent, restructure the way income tax is collected, or in a new proposal, set separate rates for real property and personal property taxes. The latter proposal could generate up to $10 million for the county, he said, and two-thirds of that amount would come from utility companies.

The executive also repeated his idea of trying to get the state to permit Prince George's to add a penny to the state sales tax, a proposal that many of the legislators oppose as politically impossible.

Glendening also said he would be willing to accept a "sunshine clause" or limited taxing authority as a temporary solution.

Chief Administrative Officer Ken Duncan and Budget Director Robert Duncan, both of whom served under Hogan, disputed arguments advanced by some legislators that the county could further cut spending or cover increased costs with the surplus. Ken Duncan said this year's surplus would amount to about $5 million, only a quarter of the surplus of three or four years ago, and that all of it is "virtually committed" because of recent court decisions ordering the county to beef up personnel at the county jail and to rehire jail guards fired in the wake of a 1980 strike. The county also faces increased health insurance costs, and unemployment compensation to most of the 507 teachers laid off last spring.

Glendening told the legislators he has taken a number of steps to save money, and has met with labor leaders and the executives of other Maryland counties in an effort to seek solutions.