Covering fire do worked, but it has nothing to be done with the suppression effect.
You could use a Garand to have some pretty nice covering fire, let's say you see a few enemies trying to advance across a street, just keep firing into the air and they won't dare to cross. (of course, this only works if you have teammates with you), then your teammates could charge ahead and toss some grenades with less chance of getting shot mid-way.
If you see an enemy guy behind a window or what, just keep firing so he won't dare to pop his head up, and when he pop up, of course he got killed! A bit spammy I must say, but effective if you have teammates covering you.
The Bren is pretty good at laying suppressing fire as well, I found the MG34/42 a bit too blinding for my like, but of course they are super-effective at pinning the enemies down. When laying suppressing fire, the taboo is to spray and pray, never do that unless you're with a tripod MG, instead just do it the semi-automatic/burst-fire way (like the pace slightly faster than firing a bolt-action rifle). If I see someone spray I'd be confident to get out of cover and shoot him with a rifle round because he isn't going to hit me like that.
I never tried it with the BAR - but in general I never know how to use that thing effectively. I just can't hit even in normal circumstances (after 2.2 of course, as the BAR in 2.2 is rather a god-like weapon).
Suppressing fire is totally useless in the case that you don't have a few guys to be with you, because they'll take advantage when you reload (and your benefit from laying suppressing fire is obviously rather limited), but if your enemy know that you have a couple of guys over there, they won't really be sure whether you are reloading or not.
In many cases, especially when outnumbered, I prefer to stay silent and not to fire unless necessary. I almost never use suppressing fire in 64 but in 128 it is a rather good thing to do. (that is, it is easier to "rambo" with less players, so teamplay elements are not as important)