Born in Eaton Rapids, Michigan, Coffey earned her B.S.L.A. in 1917 and Masters of Landscape Design in 1919 from the University of Michigan. From 1921 to 1922, she worked in Warren Manning’s Cleveland office before relocating to New York City to work in Ellen Shipman and Marian Coffin’s offices. Coffey practiced privately from 1928 until she was named Chief of Tree Plantings for the New York City Department of Parks in 1936. She continued in this role until 1942, when she returned to private practice, partnering with landscape architects Cynthia Wiley and Alice Ireys until 1944. Coffey operated her own practice from 1945 to 1957, during which time she studied public housing. In 1957 she established the partnership of Coffey, Levine and Blumberg, which designed a number of playgrounds, including Yellowstone Park in Queens and Haffen Park in the Bronx. With a keen knowledge of plants and trees, Coffey redesigned the Vale of Cashmere in Prospect Park and did rehabilitation work in the southeast portion of the Central Park Conservatory Garden. In her redesign of the Park Avenue Malls in 1970, she opened up the space by replacing fences and tall hedges with flowerbeds, and planted Kwanzan cherry trees and seasonal flowers.
Coffey had an interest in historic preservation and was involved in the restoration of Boscobel, a Federal-era estate in Garrison, New York. In 1977, she was appointed to the Art Commission of New York City as its professional landscape architect. In 1978 she became a Fellow of the American Society of Landscape Architects. Coffey is memorialized by the eponymous Clara Coffey Park on Sutton Place in New York City, where a granite marker dedicated to her is surrounded by a lush community garden. She died in 1982 in New York.