Personal opinion on Conquest Support picks. Read the notes. If I didn't list someone you use, sorry, I probably haven't used them in Support yet.
Sobek for his anti-heal, added protections, and easy to use combos as well as getaways.
Khepri for his DoT, his Resurrection, and his grab, which can turn around an enemy's tower push.
Hercules for his muscles. Massive damage output when built with Sledge+Gladiator's. Ult. for runaways.
If not Herc, Chaac. Less MP5 worries with the passive, great mobility, and huge damage. Build like Herc.
I'm a Ganesha noob, but his Silence and buffs are pretty stacked. Ult. is strange but do-able with his stun on the borders.
Kumbha noob as well, but this man slaps. CC combo similar to Apollo, Ult. like Heimdallr. Build him tanky and surprise them with some power.
Kuzenbo is seeing a lot of play right now in Casuals. His Ult. is hard to direct, but can push people on and off of Obj. pretty well.
Another one seeing more light lately, Fafnir is fun as ****. Build a speedy boi tank with CCR and you're golden.
I don't care for Cerberus, but that's bound to change. I can't help with builds but he's been decent lately from what I've seen.
Ymir is my baby, but he's running a little... meh(?) compared to early S7. He still does the damage and CC like a madman, but with more counters being present lately.
Xing Tian is a newer pick for me, but I love him. His Ult. (without Beads) is a perfect duo/jungle pluck during aggressive pushes. He's also very hard to catch with his double "dash" and wide CC.
Yemoja is a MagUardian. Some little heals for emergencies, decent damage when accurate, and a nasty trap Ult.. Different, but effective.
Terra is a very recent pickup of mine, and she is just epic in teamfights when built right. I go for GB/Reinforced Shoes/Shield of Regrowth out the gate and she is beefy.
Bacchus go brglrglrgl tank rglrglrgl belly flop drink rglrgl
Ares is still a good all around pick, just watch for Bead's cooldown when possible for Ult..
Geb is a bit different, but the CC/Support with 75% Crit. Damage received is hard to pass on in some scenarios.
I prefer seeing Cthulhu in Solo, menacingly, but he is still alright, especially with the Ult. to Obj. pushes in late game.
Artio is a favorite of mine, but she uses quite a bit of mana compared to others. Her 6 skill set is very Heal/Stun/Push/Repeat but can be used in a lot of matches.
Another one I like seeing Solo (or Jungle hehe), Cabrakan has his uses, but can be easily avoided in quite a few Support v Support matchups.
Achilles can be a Support, but I only do this when we have a magic damage Solo. Build him tank-y, get The Sledge, and don't take off the armor unless you've got two well built tanks.
Athena and Horus are lower for the same reason, their Ults. are very slow and iffy. Especially Horus. Not necessarily bad picks but I avoid them.
Jormungandr belongs in the Solo lane if you ask me. If you can pull him off as a Support, more power to you.
siiigh... I love Sylvanus, but as I was just attempting to Diamond him I realized... either I'm using him wrong, or he's meh. CC ****ing champ, better than Ymir, but you need to know what you're doing, and you need to keep a close eye on enemy combat patterns. Definitely a "wait and see" type of pick right now.
Edited on Jan 16th. I don't consider Aphrodite a Conquest Support, I use her as a Joust Support with a good tank-y Warrior. She can be used in Conquest but I don't recommend it for serious matches.