If you narrow it down to coach success, its even more rare.
Georgia Southern - the only team outside NDSU that can claim any kind of generational dominance. Three coaches won six nattys over 16 year stretch. Although they didn't win another their last 13 years in the division, they still made the playoffs seven more times plus a natty trip with a fourth coach.
FCS from '82-'13; 6 nattys
3 coaches won nattys in 85, 86, 89, 90, 99, 00
YSU - All four of YSU's nattys are thanks to Jim Tressel who coached at YSU from '86-'00. In his 15 years, YSU won four championships and made the playoffs 10 times. In the 30 years outside of Tressel's YSU coaching career, YSU made the playoffs nine times with one natty appearance in '16.
FCS from '81-pres; 4 nattys
1 coach won nattys in 91, 93, 94, 97
App State - All three of App St's nattys came in a three year period from one coach. The argument could be made also that two of those were on the back of one player. Granted App has always been a decent team, making the playoffs 20 times in their FCS history, with 18 of those coming from their championship coach. In the 11 years before his arrival, they had made the playoffs twice.
FCS from '78-'13; 3 nattys
1 coach won nattys in 05, 06, 07
EKU - A dominant team in the very early stages of the FCS playoffs, winning two of the first five FCS championships, both from the same coach After that, not so much. Their natty coach, made the playoffs 13 more times over the next 20 years, but never making it back to a natty. In the last 23 years since his retirement, they've returned to the playoffs six times.
FCS from '78-pres; 2 nattys
1 coach won two nattys in 79, 82
JMU - One of the most consistent teams outside NDSU and GSU, but still only managed two nattys, 12 years apart. Not too great before their first, only making the playoffs five times in their first 25 years. Even in the 12 years between nattys, they still only averaged a playoff trip every other year. After the '16 natty though, they made the playoffs every year till their FBS jump.
FCS from 80-21; 2 nattys
2 coach's won nattys in 04, 16
Marshall - Their FCS history lasted 19 years with the first nine being abysmal, missing the playoffs every year. Their Jeckyl and Hyde FCS tenure took a turn in '87 though and over the next 10 yeas they made 8 playoffs and six natty appearances, winning two. Their success largely came from one coach who took over from '90-'95, appearing in four nattys and winning one. A new coach took over in '96, their last year in the FCS and im pretty sure i dont have to say why they won that one.
FCS from '78-'96; 2 nattys
2 coach won nattys in 92, 96
MSU - we all know how shitty they were for long. One lucky year in '84 and then nothing for 41 years.
FCS from '78-pres; 2 nattys
2 coachs won nattys in 84, 25
UM - The most consistently playoff bound team in the FCS, especially since winning their first in '95 after making the playoffs for a 6th time in their first 18 years in the FCS. Since then in the last 30 years, they've missed the playoffs only five times, reaching the natty seven times, winning one more. In that stretch seven more different coaches have led the Griz to the playoffs and three of them leading the Griz to a natty appearance.
FCS from '78-pres; 2 nattys
2 coaches won nattys in 95, 01
SDSU - Has been considered a powerhouse of late but it took them nearly two decades to earn that. In their first 19 years they made 11 playoffs before winning their first in '22, all under the same coach. Their 2nd came a year later from a new coach but now he is gone and their season took a bit of a dive. Some are wondering if they will maintain or if the decline after their peak has began.
FCS from '04-pres; 2 nattys
2 coaches won nattys in 22, 23