At Level 60 you can pick up the quest Plants of Zangarmarsh from Lauranna Thar'well <Expedition Cataloguer> in Cenarion Refuge.

Collect 360 Unidentified Plant Parts from grinding mobs or the auction house.
Turning in Plants of Zangarmarsh gives 250 rep.

After turning in Plants of Zangarmarsh the repeatable quest Identify Plant Parts becomes available.

Turning in Identify Plant Parts gives 250 rep.

Inside of the Package of Identified Plants that you receive, there is a 5% chance to get an Uncatalogued Species which starts the quest Uncatalogued Species.

Turning in Uncatalogued Species gives 500 rep.

36 turn-ins of the Unidentified Plant Parts should give you 1 or 2 Uncatalogued Species, effectively lessoning the amount of Coilfang Armaments you’ll need to cap off your rep later.

36 turn-ins of the Unidentified Plant Parts gives 9000 rep.
2 turn-ins of the Uncatalogued Species gives 1000 rep.

You should start questing at around 1000/12000 Honored.

From 60 to 67 the only way to gain rep is by doing quests. You can gain a miniscule amount of faction by running Underbog and killing Hungerfen after Honored level, but it’s probably not worth it to go out of your way to do this.

At level 67 you can pick up Orders from Lady Vashj to start the quest Orders from Lady Vashj. They drop off trash mobs in Steam Vaults.
Turning in Orders from Lady Vashj gives 500 rep.

After turning in the Orders, Preparing for War becomes available. Collect Coilfang Armaments from Steam Vaults, or the auction house.
Turning in Preparing for War gives 250 rep.
Subsequent turn-ins give 75 rep

Depending on the amount of questing you’ve done before being eligible for Steam Vaults, you can get into Revered with Cenarion Expedition. Assuming you did not get any rep between the turn-ins at level 60 and now after picking up your Orders from Lady Vashj, you would need 32,000 rep to go from 1000/12000 Honored to Exalted. Subtracting the 500 from the Orders from Lady Vashj turn-in and 250 for the initial Preparing for War turn in, you’d need 31,250 rep, or 418 Coilfang Armaments to reach Exalted. (1 Armament for the initial turn in plus 417 to push past 31,250 into Exalted)