So I'm currently level 18 on my Cowboy role-play and I really can't figure out what weapons to use... Hes built around sneaking and sniping but he can easily use melee weapons as well.

I prefer to keep my loadouts at a Long range weapon, a short range weapon, medium range weapon, and a back up melee weapon.

Current loadout:

La Lounge Carbine (Long Range)
Mysterious Magnum (Short Range)
Chances Knife (Melee Backup)
Brush Gun (Medium Range)
Dynamite (BOOM)
Pulse Grenades (Robots!)

Should I possibly switch some out for others?

La Lounge Carbine (Long Range) <-- Switch that out for a Trail Carbine with a scope mod and SWC ammo. Allot more damage on target and hardly ever needs repairs.
Mysterious Magnum (Short Range) <-- Find the .357 revolver called 'Lucky'. Evil handgun with a character that has a modest base critical hit chance.

Toss in a Lever-Action Shotgun with magnum buckshot. It's light weight and quite powerful in it's own right. Add 'Shotgun Surgeon' perk for a total of -12DT effect.

And get Knock Knock to, the thing is a beast of a melee weapon.

Whenever I go cowboy I always get frustrated that I can't get a Bowie Knife, but the Cosmic knife (uncleaned) comes pretty close.

Completely forgot about Lucky thanks for that! And I tried the Trail Carbine with a scope but I just didn't care for it too much... I wish the hunting rifle counted...

Chance's Knife should be close enough. Pretty crazy damage output with both Grunt and Cowboy perks.

But the Combat Knife looks way more like a bowie than the cosmic knife.

And like Kor'Ah said Chance's Knife is powerful and a cool version of the Combat Knife that's covered in blood.

That Gun and Ranger Sequoia come to mind.

Cowboy build needs a brush gun for medium range, a brush gun for short range, a brush gun to use on robots, and a brush gun for melee range.

Seriously, unless you're just trying to make the game harder on yourself, for the sake of "style. A brush gun will work for 100% of all situations.

Long range?? Screw long range. Sure, the Brush Gun is a decent sniper, but forget that. Just run up and give them a taste of some medium range justice!

In case you need actual numbers to back it up, the base damage for Brushy (75) is higher than the crit damage of Lucky (60). The mysterious magnum crits (80) are just a teeny bit higher than a Brush normal hit (75). The only pistol that's even in the same ballpark as the Brush Gun is the Ranger Sequoia (63) and hunting revolver (58). And that's just cuz they fire the same bullet. With Cowboy and Handloader bullets, Brush Gun does more damage per bullet than the AM freaking R. Plus has -6 DT.

I'm gonna repeat that last bit, cuz it bears repeating: a Brush Gun, with Hand Loader rounds and the cowboy perk, does more damage per shot than the AMR.

Or, to put it all more simply; why carry 6 mediocre weapons? One awesome weapon will suffice.