Mrs. Elizabeth Morris Smith of Newport, R.I. and Palm Beach, Fla. has announced the engagement of her daughter, Alletta Morris, to William J. Cooper, Jr., the son of Mr. and Mrs. William J. Cooper of New Haven, Ct. and Long Boat Key, Saracosta, Fla.

The future bride was graduated from Notre Dame Academy (Va.). She is the granddaughter of the late Lewis Gouverneur Morris and Nathalie Lorillard Bailey Morris of Newport and New York, N.Y., and a direct descendant of Lewis Morris, signer of the Declaration of Independence, and a niece of Mrs. Peter McBean of Hillsborough, Cal. and Newport. Her father is Morton W. Smith of Middleburg, Va., horseman and breeder of thoroughbred horses.

Mr. Cooper operates a publications consulting firm in Newport, R.I. and New York City. He was an Assistant Manager and Assistant to the Vice-President of Sales and Operations of the Washington Post.An alumnus of the Pomfret School and Duke University, Mr. Cooper was graduated from Boston University. His father, before his retirement, was Chairman of the Board and chief executive officer of The United Illuminating Company of New Haven, Ct. Mr. Cooper is the grandson of the late Mrs. Ethel Lewis Busing of New York and Clearwater Beach, Fla. and the late Richard Bolton Arrington of New York and Petersburg, Va., and the late Mr. and Mrs. C. Walter Cooper of Columbus, Ga. and Daytona Beach. His previous marriage was terminated by divorce.

A June 27th wedding is planned.