The only space where New York's homeless children can feel assured of permanent lodgment would appear to be the state Supreme Court docket.

Two and a half years have passed since state supreme court Justice Edward Greenfield told the city to provide beds, cribs, towels and like luxuries to those displaced families lucky enough to be quartered under its emergency shelter program.

The city unhesitantly filed an appeal. The subsequent 14 months of inaction aroused Greenfield to order the Department of Social Services to get moving.

"The defendants the city argue," he scornfully noted, "that they have no obligation to provide emergency shelter for the homeless. This, from the city whose Statue of Liberty . . . proudly proclaimed: 'Send these, the homeless, tempest-tossed, to me.'

"Providing a homeless family with a hotel room -- often a cubicle . . . infested with vermin . . . children sleeping on the floor from lack of cribs, an entire family sleeping in one bed is unacceptable shelter for anyone, especially families with young children. . . . If convicted criminals have rights to minimal shelter, the homeless who become interim wards of a governmental entity are entitled to no less."

These sentiments would appear to be unexceptionable enough for a mayoral campaign speech; the city nonetheless appealed from them, and now, 16 months afterwards, a supreme court appellate division is at last ready to entertain its objections.

Mayor Edward Koch has often taken public pride in his city's shelter program as the country's best. Any compliments based on that comparison would be small ones indeed, and, in any case, the mayor sensibly forbears to remind his auditors that pretty much everything he has done to engage this worsening emergency has been forced on him by the courts.

The first successful shelter suit was brought in the cause of homeless men. When its appeals ran out, the city grudgingly complied with the letter of the court order, while declining to extend its rough grace to homeless women until the appellate division told it to.

The rights of lone grown men were established first; lone grown women followed, and now mothers and children await their turn. The order of precedence for even the coldest and coarsest of our welcomes to these outcasts of our streets is established in inverse ratio to each one's vulnerability.

The case of Edna M. strikingly illustrates this curious notion of priorities. She has a 9-year-old child with measles, is seven months pregnant and has no place to live.

Recently she repaired to one of the City Human Resources Administration's emergency assistance units in search of shelter. None was available, and Edna M. and her ailing child spent the next two nights sleeping in the emergency assistance unit on the Formica tables and under the fluorescent lights that are among the amenities unique to this particular hostel.

Under ordinary circumstances, Edna M. and her child might well have been dispatched to the Roberto Clemente Shelter, the city's major transient facility for families. They happened, however, to be barred by the shelter's not implausible restrictions on entry.

Edna M. is advanced in her pregnancy and Roberto Clemente excludes women in that condition because its ambience is too risky for them. She had, moreover, a sick child with her, and Roberto Clemente refuses to give house room to applicants with contagious diseases.

And so, Edna M. and her child had failed to qualify for the best the city has to offer the poor, not because they were not in trouble enough but because she was too vulnerable, her child was too sick and they were both too needy. Come unto our city, you heavy-laden -- but take care the load isn't too big.