Beckman began coaching as an assistant at his alma mater, Baldwin–Wallace College. From there he coached at University of Evansville and spent the years of 1973 through 1978 at the University of Iowa.
Beckman was named director of player personnel for the Hamilton Tiger-Cats in April 1990. During that season, Beckman was promoted to interim head coach when Al Bruno was fired with six games remaining. Beckman finished with a 2–4 record. He began the 1991 season as head coach, but was fired on August 30 after going winless in the team's first eight games. He was replaced by John Gregory, who had been fired by the Saskatchewan Roughriders earlier that season.
- Rick Matsumoto (25 September 1990). "Ticats 'pull the trigger' and fire coach Bruno". Toronto Star. p. B4. Retrieved 14 February 2011.
David Beckman has become the interim coach. ...
- "Transactions". The Milwaukee Journal. 1990-04-18. p. C6. Retrieved 2015-09-09.
- "Transactions". Spartanburg Herald-Journal. 1990-09-25. p. D4. Retrieved 2015-09-09.
- "SA coach refuses Hamilton position". The Victoria Advocate. AP. 1991-09-01. p. 5B. Retrieved 2015-09-09.
- Supinie, John (2012-08-26). "Illini's Beckman followed father into profession". State Journal-Register. Springfield, Ill. Retrieved 2015-09-09.