I am not sure how helpful I can be. You could brand me as one of those people who plays a mage as a support. I've usually played solo lane or jungle so when I need to support I go with a mage because I feel like it's better for soloq and I'm more experienced on mages than supports.
Karma has an easy skillshot which offers significant poke, it does great damage the entire game. Her shield and root offer great utility and kiting for you and your team. She doesn't require high level mechanics and doesn't take much practice, if any, and the only skillshot she has is her Q and it's medium difficulty to hit it normally and very easy when you RQ. When enemies go HAM on you botlane you have shield+MS buff to save you or your ADC along with W to root them if they chase after you. She's mobile as she can chase and escape with the same abilities.
Annie has good burst and guaranteed damage. Her Q is easy to spam and to harass with and it's not even a skillshot. Her auto range is also ridiculous so it's very easy to poke down the enemies. Level 6 her ult means instant death for the enemy lane if they're at 50-70% hp and you have flash up. She's easy to play and scales well into the game.
Like I said in the beginning this isn't the support support playstyle where you pamper your ADC, this is the mage support playstyle where you kill your enemies and become a secondary APcarry. The important thing is that even though you bring a lot of damage you still bring support utility with Karma shields/roots/slows and Annie aoe stuns. You also still build sightstone and buy pinks.
I included Annie mostly because her damage/cc is pretty much guaranteed and she doesn't really require any skill(compared to Nami/Morg/Thresh). I wouldn't say she's a "learn how to sup" champ but she is easy to support with.