At a sunrise Easter service for the homeless today, they were asked to forgive the city fathers for engaging in what was described as a systematic program to arrest and prosecute them ''merely for sleeping.'' The plea at the service in City Hall Park by the Rev. Alan McCoy, former pastor of the Santa Barbara Mission, also urged reconciliation rather than confrontation in the continuing battle between the city and its homeless people. Santa Barbara, unlike other cities that have found different ways to handle the problem, has reacted with stern measures to an influx of homeless people here. In 1979, the city passed an ordinance banning sleeping and camping in public places. That ordinance was followed by others outlawing drinking in public and banning the homeless from voting in elections. The City Council defeated a proposal that would have outlawed the removal of food from garbage cans. In the last 16 months, at least 1,000 homeless people have been arrested for sleeping in city parks and on streets and beaches. In the same period, two homeless men were killed and two youths arrested in one of the slayings. But Mayor Sheila Lodge defends Santa Barbara's policies toward the homeless, saying the city does as much, if not more, for the homeless than other cities in the country. Defying an Ordinance About 150 homeless people held a candlelight vigil in City Hall Park Saturday night and slept there overnight, defying the ordinance. But this time the police made no arrests, in part, said Colleen Duncan, who helped coordinate the vigil, because the city gave the group a permit to stay overnight. ''But not to sleep,'' she said. Miss Duncan said the vigil was designed to alert President Reagan, who was at his ranch in the Santa Ynez Mountains 29 miles away, of the need for Federal money to help the nation's needy. The theme at the Easter service followed that of protests by the homeless who say Santa Barbara has tried in every possible way to force them out. Last week, Mitch Snyder, a national advocate for the homeless, came to Santa Barbara to say the city was the ''worst in the country'' when it came to helping the homeless. Mr. Snyder is director of the Community for Creative Nonviolence in the District of Columbia, a group whose tactics include civil disobedience and mass demonstrations to spur change. Mr. Snyder, whose life story is soon to be broadcast as a television movie, threatened last week to inundate the city with thousands of homeless people if Santa Barbara did not change what he called its ''ignorant and selfish ways.'' editorial in The Santa Barbara News-Press, the city's daily newspaper, called Mr. Snyder a rabble-rouser and said he had ''turned homelessness into a profession.'' Over the last two years, some 1,250 citations have been issued to homeless people for sleeping in public places. Many were jailed because they could not pay their fines. The police are also arresting homeless people for sleeping in abandoned buildings ''without the permission of the owner.'' 'Sick and Tired' Against this backdrop came the slayings of two homeless men. The police say they have not found the killer of the first victim, Kenneth Burr, 35 years old, who was shot in the head. They did arrest two youths in the slaying of Michael Stephenson, 29. Last week David Kurtzman, 18, one of the suspects in the death by stabbing of Mr. Stephenson, was found guilty of second-degree murder. A second defendant, James Tramel, 18, is awaiting trial. ''We are sick and tired of watching and reading and hearing of the vulgarity of the treatment of the homeless in Santa Barbara,'' Mr. Snyder said. ''This is too wealthy a piece of ground. There is too much here for you to say, 'Get out of town.' '' Mayor Lodge said in an interview that Santa Barbara is not the wealthy bastion everyone perceives it to be. While there are great pockets of wealth, she said that on the basis of its median household income, its residents were poorer than those throughout the state. She also took issue with statistics that put the city's homeless population at between 1,500 and 2,000. The Mayor said that the city had spent roughly $40,000 of its $250,000 social service budget for a 40-bed shelter that will be operated by a nonprofit group and will soon open. The city runs no shelters for the poor. In addition, the Mayor said, religious and nonprofit agencies provide a 100-bed shelter and food for the homeless. Virtually all of Santa Barbara's ordinances have been challenged in court by the Legal Defense Center, a private group. The center was successful in overturning the ordinance barring the homeless from voting.