Riordan's availability is great and he is a very strong unit from early to late game due to his personal skill. He is the first person who can fully utilize the Love Ring and that can really help a Demonic playthrough. He does tend to need some help even in specific classes that he is strong in because he will fail to meet one rounding potentials in Demonic without favoritism. Speaking of favoritism, I would avoid using any Elixirs on him and just settle for the Bloodied Ring.
Riordan has A LOT of different options open to him. He performs well in every single tier 2 class he has. His personal skill takes effect after the first hit, so if he doubles (or quads), this will increase his kill potential by quite a bit. The defense shred persists after combat as well, so he can set up kills for other units.
Ranger - Riordan will be slow and in Demonic he generally will never kill, but instead survive a hit or two and set up kills for allies all while stunning another threat with Lanky Spanky (and Command Orangutan actually increase crit chance a bit more than you would think in Demonic).
Cuttthroat - It is no secret how busted Licky Lasso is, but Riordan has really good luck behind Eve and makes well use of the passive. Command Toad is decent at applying poison if you need it; though generally, you'll never touch it.
Tamer - Riordan is surprisingly bulky and while he won't kill much of anything, the 1-2 range is nice and his defense shred does scale with Tamer passive.
Quickdraw - Riordan becomes quite a monster when you pair him with a Repeater. All of a sudden, he can suddenly start quadding things even in Demonic, though obviously not everything.
Side Note: Riordan makes great use of the Love Ring early on (especially true as a Ranger or Tamer) as he is the first to have access to all 4 of his bond supports. I'd recommend going any one of his tier 2 classes depending on your needs in the early game and then once you hit 25, reclass him into Cuttthroat due to his high luck stat, before you put him into one of his preferred tier 3 classes.
Riordan's Tier 3 options are another story.
Slayer - With Slayer (and specifically the Karambit dagger), Riordan is a monster. He can't quad everything, but there is quite a bit he can quad! Additionally, just giving him a strong dagger in Demonic, he can still do a lot of damage and even secure kills - especially when Slayer passive works. You can be an RNG god going all in with Ricochet passive and the Blazing/Soulfire/Drunkard Rings, or you could go all in with Scrapper passive and play a safer variant of Slayer with Archmage and Diplomat Rings.
Deadeye - With Deadeye, Riordan is still a beast. Having access alone to Wing Buffet alone let's him set up a ton of shenanigans for both him and his team. The Archmage and Companion Ring are really nice to have on him to be able to use his skills.
Beastmaster - Beastmaster is surprisingly a better tank than Warden due to Riordan being able to spam his personal skill more (thanks Beastwhisperer passive) while still being somewhat tanky and having 1-2 range; but overall, not amazing. Pairing him with the Love and Dimming Rings increases his overall bulk significantly and makes him a decent frontline tank/setter for your team.
Note: the "Overflowing" Rune on Karambit is probably a lot better than the "Deadly" Rune due to Ricochet.