Personally I don't think the Firebug really needs a whole new weapon. Sure it'd be pretty nifty if he got something new, but I think some of his issues should be addressed first.
The first problem imo is that the fire doesn't act as you'd expect. For example, if you shoot the flamethrower on the floor BEFORE a zed, the fire stays there for a second or so but it doesn't light the zed on fire - it'll walk through it unscathed. This is quite disorienting since it's difficult to tell if the zed is lit up or not when he's walking through the fire. It'd be nice if this issue was fixed so that either the zed gets lit on fire or if "missing" with the flamethrower doesn't leave a burning residue.
The next problem is the strange-acting recoil. When looking down the "iron sights" of the flamethrower, sometimes you'll get a really sharp recoil while most of the time, there is nothing. I have no idea if this is supposed to be realistic or if it's just glitchy but no other class has to suffer from this problem. The firebug's damage isn't high enough to warrant this unpredictable recoil.
Third - once you reach level 3 or whatever, you become immune to fire. If you light up a zed who is close to you, you also get lit on fire but take no damage. Yet there is still an obscuring fire animation played on you for a few seconds. Fairly annoying and I see no reason for it - you aren't taking damage so why the visual feedback?
So I think those 3 issues are the major ones that just make playing firebug a pain and not worth the trouble. His damage isn't nearly high enough for the trouble in my opinion.
As for suggestions on how to 'beef' up the firebug, my suggestion is that his flamethrower should be upgradeable. The trader can have like 8 or so 'upgrades' that you can choose, but you can only install 2 or whatever. Maybe divide the Flamethrower into 3 parts (nozzle, fuel and canister?) and you can upgrade each. Some examples:
Canister Compression - Increase ammo capacity by 25%
Active Pressure Nozzle - Increase range by 25%
White Phosphorus Napalm - Increase burn time by 50%
Thickened Pyrophoric Napalm - Increase damage by 25%
Carbonite Reload clips - Decrease reload time by 25%
White Polymer Additive - Flames become nearly invisible for enhanced visibility
Canister Ejection Module - Adds an alt-fire mode, which launches out a canister and explodes. Uses an entire canister and the power of the explosion depends on the canister's ammo amount
etc. add your own ideas!
edit: I also find the Firebug's capability to make a zed flee in panic when on fire to be a very interesting and useful mechanic. But, I think it's a bit too unpredictable to be all that useful. Therefore, I think there should be a weapon designed to specifically cause that to happen in all (most?) zeds; maybe make it so when a firebug grenade goes off, all zeds lit on fire with that will do their run-around-screaming animations (maybe even fleshpounds?) Or, add a new weapon, like the molotov cocktail suggestion.