A quality of good feeling that compensates for awkwardness; Bing and Walker, Play by James Paul Farrell. Directed by Dan Bonnell.

A congenially casual backyard, scene of countless American dramas of family and other relationships, provides the milieu for ''Bing and Walker,'' the Circle Repertory Company's latest offering. Playwright James Paul Farrell locates his particular backyard in Woods Hole, Mass., the state that's home to the bean and the cod - and the Woods Hole Oceanographic Institution. Mr. Farrell's is the only play I can recall to use the institution for dramatic purposes - albeit offstage.

The Circle Rep has varied the backyard scene slightly by creating a semicircle seating arrangement around David Potts's unpretentious setting. In keeping with its penchant for the environmental touch, access to the auditorium is via the corner of a cluttered barn and across the green grass of Ellie Walker's backyard. Ellie (Stephanie Musnick) is the elder and obsessively caring sister of Arthur Walker (Jack Davidson), a retarded adult with whose confusions and childish willfulness she has learned to cope.

Enter Diane Bing (Samantha Atkins) and elder brother Eddie (Edward Power). With bratty but beguiling officiouness, Diane has determined that Eddie should resume the courtship of Ellie which Ellie's late mother had quashed. To free Ellie, Arthur must prove himself capable of leaving home for a proffered deckhand's job on an Oceanographic Institution vessel. And Ellie must be persuaded to let him go and to live her own life.

Mr. Farrell takes his time working out his characters' common and uncommon problems. On its way to resolution, ''Bing and Walker'' involves recriminations and confrontations - by turns comic and violently emotional. Dramatic progress is marked at times by a certain lack of facility. To cite a technical point, the unseen gift shop that Ellie operates in the front of her Cape Cod house provides the author with exits that serve both contrivance and convenience.

Yet there is a quality of good feeling about ''Bing and Walker'' that compensates for some of its awkwardness as drama. Mr. Farrell clearly respects his quartet of Cape Codders, enjoys their catch phrases and small rituals, sympathizes with their problems, and takes a hopeful view of their possibilities. Under Dan Bonnell's direction, a solid Circle Rep cast responds to the quality and temper of the play. Design requirements are handily met by Mr. Potts (the hospitable set), Mal Sturchio (lighting), and Deborah Shaw (costumes).