Successfully complete the indicated task to unlock the corresponding weapon:

-=Lasso=-
Lasso: Obtained during the "Wild Horses, Tamped Passions" mission. 

-=Pistols=-

Double-Action Revolver: Clear out the Tesoro Azul Hideout.
High Power Pistol: Obtained during the "Bear One Another?s Burden"
mission.
Lemat Revolver: For sale at the Escalera Gunsmith for $1,250 after
the Revolution.
Mauser Pistol: For sale at the Blackwater Gunsmith for $800.
Schofield Revolver: Obtained during the "The Gunslinger?s Tragedy"
mission.
Semi-automatic Pistol: Clear out the Fort Mercer Hideout, and it
will be for sale at the Escalera Gunsmith for $300.
Volcanic Pistol: Clear out the Twin Rocks Hideout, and it will
then be for sale at Armadillo Gunsmith for $100. 

-=Projectiles=-
Dynamite: Obtained during the "Father Abraham" mission. It will
then be for sale at various stores.
Fire Bottle: Obtained during the "The Demon Drink" mission. It
will then be for sale at various stores.
Throwing Knife: Obtained during the "The Great Mexican Train
Robbery". It will then be for sale at various stores. 


-=Rifles=-
Bolt Action Rifle: Obtained during the "The Gates of El Presidio".
It will then be for sale at Escalera Gunsmith for $750.
Buffalo Rifle: Reach Master Hunter Rank 5, and it will be for sale
at any Gunsmith shop for $475.
Evans Repeater: For sale at Blackwater Gunsmith.
Henry Repeater: Clear the Nosalida Hideout.
Repeater Carbine: Obtained during the "New Friends, Old Problems"
mission.
Springfield  Rifle: Obtained during the "We Shall Be Together
in Paradise" mission, or clear the Gaptooth Breach Hideout. It
will then be for sale at Thieves' Landing Gunsmith for $300.
Winchester Repeater: Clear out the Tumbleweed Hideout, or
successfully complete "Spare the Rod, Spoil the Bandit" mission.
It will then be for sale at Armadillo Gunsmith for $350. 

-=Shotguns=-
Double-barreled Shotgun: Obtained during the "Spare the Rod, Spoil
the Bandit" mission. It will then be for sale at Armadillo
Gunsmith for $150.
Pump-action Shotgun: Obtained during the "And the Truth Will Set
You Free" mission.
Sawed-off Shotgun: Clear Pike?s Basin Hideout. It will then be for
sale at Thieves' Landing Gunsmith for $250.
Semi-auto Shotgun: For sale at Escalera Gunsmith for $1,000. 

-=Sniper Rifles=-
Carcano Rifle: For sale at Blackwater Gunsmith for $1,100.
Rolling Block Rifle: Obtained during the "Empty Promises" mission.