FATE bosses are usually not too bad in terms of DPS they inflict (there are one or two exceptions like Behemoth) - you can probably get by with just a Chocobo Companion healing you. My Arcanist's Carbuncle was tanking them easily back in the day, and you can usually solo a FATE boss as long as you have some form of light healing and means of dealing damage (Any tank with a Chocobo, SMN with pet, etc)
I'd back Urthdigger up on the variety idea - it'd be most efficient to have one Tank, one DPS and one Healer; but if you all want the ability to deal decent damage I'd suggest Warrior and Scholar. WAR are still a bit better than PLDs in low-man content, and SCHs can get some very decent DPS from their DoTs whenever accuracy isn't an issue (basically everything aside from Coil). If one of your friends is dead set on not being a tank - I'd suggest Summoner (Caster) and Scholar (Healer) since in a pinch you can have Titan-Egi tank for you.
