I think Conquest is a good candidate for special loadouts, because it has many weapon slots and ordnance points, good base flux dissipation, and good mobility.
Some people will leverage Conquest mobility mostly as a way to kite slower opponents while shooting with long-ish range guns (and maybe missiles). One seemingly popular loadout for this is the so call “sniper build”, with 2 Gauss Cannons on one side, and defense/empty other side.
A few people like to put Heavy Blasters on Conquest. Here mobility is used in a completely different way.
I like my Conquests to be mostly “balanced”, so I always use symmetrical loadouts, usually with Pulse Laser + Mark IX + HAC + Hephaestus/Hellbore + Flak. Sometimes I don’t put any missile. Sometimes I put 1 or 2 Locust. Nothing unusual, right? Sometimes I go crazy and put 1 or 2 Cyclone Reaper Launchers or Hammer Barrages, as a bust damage anti-station solution. Together with Auxiliary Thrusters and good use of the ship system, it is possible to rotate the ship to aim the large missile launchers at the target, fire a volley of torpedoes, then turn back to “normal” position. I remember once I chased a Doom while piloting such a Conquest, shooting Hammers at it so the torpedoes would hit it once Phase Cloak deactivates, on this occasion turning wasn’t necessary nor effective, only option was to move straight toward the (annoying) target - I guess an Ion Beam would have been useful.
Another unorthodox thing I do often is put humble Talons in my carriers (especially Legion). These aren’t perfect fighters, but I find them quite useful in many situations, and OP-cheap. Basically I feel like my fleet is more effective when it has the right amount of Talons (depending on fleet size). Their biggest downside AFAIC is the high crew casualties (even with skills). Obviously, Talons are no replacement for proper bombers.
Last thing I can think of now as uncommon, is I like to put torpedoes on my frigates, so they have a higher chance to cripple and destroy heavier targets. Yes, I do send frigates to face such targets, and not just as distraction. Specifically Hammers available right at the start of a campaign, and also Reapers. Another reason to use these, is the 1 OP or 2 OP cost, easy to fill-in an otherwise complete loadout with max dissipation and max vents. Sometimes I use the single-Sabot as a filler. I could be wrong but I am under the impression that Annihilators, Harpoons, regular Sabots and Swarmers are more popular on frigates.
Anyway, IMO it is a good idea to experiment and see for yourself what works and what doesn’t, don’t be afraid to try unusual things.