Yes, its possible. Just about every mob at Corins Crossing (i think thats the name) gives rep. It's a little rough in terms of solo'ing it but if you got a buddy with a high level toon, it's an easy afternoon.
Literally every mob at Corin's Crossing will give you rep up to 5999/6000 friendly (you only need 0/6000 Friendly to get the Tabard). After that, only Stitched Horrors and Gibbering Ghouls will give rep up to 999/1000 Exalted. Easily soloable for a fully twinked f2p hunter.