Sweatman began coaching in 1968 and coached college football for 12 years. From 1985 to 1992, he served as both the assistant special teams coach and special teams coach for the
New York Giants, and was a member of the staff that won both
Super Bowl XXI and
Super Bowl XXV. In 2004, Sweatman returned to the Giants when new head coach
Tom Coughlin hired him as his special teams coach. In 2004, the team led the NFL in kickoff return yardage for the first time since 1953, with an average return of 25.1 yards, and their average start following a kickoff was at the 30.1 yard line, the best average starting point in the NFC and fifth-best in the league. In Sweatman's first season with the Giants, the average start was the 31.8 yard line, the best in the NFL. The Giants’ punt returns also improved from an average of 5.1 yards in 2003 (32nd in the league) to 9.2 the following year, (8th). Under his watch,
David Tyree was voted to his first
Pro Bowl, and punt returner
Chad Morton was named as a first alternate.
Jay Feely, another first Pro Bowl alternate, had the then-best season by a Giants kicker, leading all kickers with a team record and career-high 148 points, the first Giants kicker to hold the top spot since
Don Chandler in 1963. Feely set career highs and tied two team records with 35 field goals and 42 field goal attempts, while punter
Jeff Feagles was a consistent and productive player in his 18th season, with a 42.1 yard gross average and a 37.0 yard net average. He retired from coaching following the 2006 season, and his assistant
Tom Quinn was promoted to replace him. ==Personal life==