Use the DMG for firearms, and ready actions for suppression
You don't need to homebrew any rules. Wikipedia describes suppressing fire as:
Suppressive fire usually achieves its effect by threatening casualties to individuals who expose themselves to it. Willingness to expose themselves varies depending on the morale, motivation and leadership of the target troops.
The attackers can ready an action to shoot at a player whenever they leave cover. You can even give them a special multiattack ability so that they can take multiple shots on readied actions. This forces players to make the consideration described in the wikipedia quote: "Do I leave cover and expose myself to being shot?"
This approach has the advantage of putting suppression in the players' minds, instead of forcing the issue mechanically.
D&D characters are brave and strong
I'm not sure that doing this in D&D 5e will have the effect that you want. Going off of the firearms page in the DMG, the damage that a gun can do is similar to that of the standard D&D weapons. It's enough to kill a commoner (you, me, a real-life soldier), but D&D characters are supernaturally strong and wise, and face much more dangerous things than gunfire while adventuring anyway.
I don't have experience with other RPG systems, but it seems that it'd be a lot easier to find a different RPG to play than to twist D&D into a realistic modern combat game.