Rivera is the second Panthers coach to win the award. Dom Capers was AP Coach of the Year in 1996, Carolina's second season in the NFL.
All-Pro Kuechly received 19 votes, ahead of Indianapolis All-Pro linebacker Mathis, who earned 11½.
Kuechly was credited with 96 tackles, four interceptions, two sacks, eight passes defensed, and was a presence from sideline to sideline on the NFL's No. 2 unit.
A second-round pick (61st overall) from Alabama, Lacy was a key performer in the Packers' offense, particularly when star quarterback Aaron Rodgers was sidelined for seven games. He rushed for 1,178 yards on 284 carries (4.1 average), with 11 touchdowns. He also had 35 receptions.
That was good enough for 35 votes.
"I'm comfortable where I am, and my teammates believe in me, and they make me feel comfortable, so I'm able to play the way I'm capable of playing," said Lacy, who beat out San Diego wide receiver Keenan Allen, who received 12 votes.
Richardson, the 13th overall pick in April's draft on a selection acquired when New York traded star cornerback Darrelle Revis to Tampa Bay, won a close race over Buffalo linebacker Kiko Alonso. Richardson received 23 votes; Alonso, a second-round choice (46th overall), got 19.
Often double-teamed as the season wore on, Richardson made 42 tackles and had 3½ sacks. He clogged the running lanes so effectively that the Jets ranked third against the run this season.
"I'm surprised," Richardson said of beating Alonso and Arizona safety Tyrann Mathieu, who got two votes. "Kiko and Tyrann most definitely had outstanding rookie years and it was a toss-up to me. Kiko made a lot of tackles and Tyrann made a lot of plays down the field. Unfortunately he got hurt, but it was a tight race."
Richardson joked about the possibility of winning both awards — he scored two touchdowns as a fullback in goal-line situations.