The probability of at least one safety per game is 5.77%, based on historical experience.
The expected number of safeties per game would be -ln(1-0.0577) = 0.0594.
The expected number per quarter per team would be 0.0594/8 = 0.0074.
The probability of exactly two safeties by the same team in a single quarter would be e-0.0074×0.00742/fact(2) = 1 in 36,505.
In an NFL season there are 267 games, and 267×8=2,136 team quarters. So, according to my estimate, this will occur on average once every 36,505/2,136 = 17.1 years.
This should be considered as just a rough guess. There are factors to the game that I'm not taking into account, in the interest of simplicity.