IN CHOOSING the adults who will become the teachers, coaches and daily guardians of children, there is no such thing as being too diligent. One must ask, then, why Eric James Long, twice convicted of sexual offenses against young boys, in 1972 and 1980, was able to get a job as a gymnastics instructor at a private school in Bethesda in 1978 and keep that job until recently. In the past two months, Mr. Long has again been charged with various sexual offenses against six more boys, ages 6 to 11, in the neighborhood around his home.

School officials have answered by blaming the judicial system. The judicial system protests that nothing more could have been done. The facts, however, are these: Mr. Long never served any prison time for either of his two convictions. In both cases, judges sentenced him to three years' probation instead, only adding the stipulation that he receive regular psychiatric treatment. Officials at the French International School were not only unaware of Mr. Long's conviction in 1972; they were even unaware of the fact that he was arrested in 1979 and convicted in 1980 at a time that he was working for the school.

School officials might consider looking up conviction records in the local court offices to discover whether a person has been convicted of any crimes. But one must also wonder how many times a person must be convicted before something is done to keep that person away from potential victims.

In October 1972, Mr. Long was convicted of sexually assaulting a young boy and was sentenced to three years' probation and psychiatric treatment. He was arrested for a violation of probation in 1975, and his probation was extended three years. He was discharged from probation in November 1977. In 1979, he was arrested and, in 1980, convicted for sexually molesting another boy. He was again sentenced to three years' probation.

Not very long ago, Arthur F. Goode III, who had been convicted three times of sexual assaults on children, was given two suspended sentences on the condition that he "voluntarily" enter a state hospital in Catonsville, Md. He subsequently was arrested and convicted of assaulting and killing two young boys.

Bills currently before the Maryland and Virginia state legislatures would require criminal-record checks of people seeking jobs at schools and day-care centers. Both states would become eligible for $25 million in federal funds to set up the screening program and would join 10 other states with similar programs. Both would represent a step in the right direction. But one would also hope that swift and not so lenient sentences would be meted out to the adults who are convicted of repugnant assaults on children.