Born in Aberdeen, Maryland, Stillson attended Campbell High (Calif.) where he was a high school all-American diver. A 1974 graduate of Ohio State, Stillson earned NCAA All-American honors his senior year in the three-meter competition. He arrived in Texas as soon as he could to follow TSDHOF inductee Bryan Robbins at SMU. In his 33 years as head coach of the men's and women's diving teams, his athletes earned 88 all-America honors, and the men's and women's teams won 32 combined conference championships. He also coached 10 U.S. National Champions, four NCAA champions, and four Olympians, including 1992 silver medalist and TSDHOF inductee Scott Donie. In 1989, Stillson was named the NCAA Men's Diving Coach of the Year, and in 1990 and 1995 he was the NCAA Women's Diving Coach of the Year. On the conference level, he has earned 15 conference diving coach of the year honors while at SMU. Stillson served as one of the U.S. Diving National Team coaches from 1987-91 and again in 1997. His successful coaching ability in 1999 earned him that year's United States Olympic Committee Diving Coach of the Year award.