Coar entered private practice in Mobile, Alabama from 1971 to 1972, then in Birmingham from 1973 to 1974.

[2] Coar served as a United States Bankruptcy Judge for the Northern District of Illinois from 1986 to 1994.

On August 16, 1994, Coar was nominated by President Bill Clinton to a seat on the United States District Court for the Northern District of Illinois vacated by Ilana Rovner.

In 2013 he was named to co-lead a commission with Benjamin K. Miller to draw a path to Bond Court reform for the state of Illinois.

The next year the commission issued a comprehensive report detailing the problems of the system and gave forty recommendations for reform.