I agree that Morgana counter for Leona in lane is not great for higher elo (See Xpecial v Kreppo in this game as example). As you stated her shields are to long of a cooldown and Leona can just q the non shielded person after zenith blade.
Looking at the raw game data is useful if you already have a good understanding of lane match ups, but that doesn't provide any insight on why certain supports are good vs Leona. It also doesn't encourage innovation in lane because everyone always plays what everyone else plays. The best approach is to know why Leona(or any champion) is weak in lane/game and find champions or gameplay that exploits that weakness.
Here are some alternative champions if Thresh and Lulu are banned.
Alistar is an often an underrated support due to his melee and higher skill cap. He's great if you're freezing right in front of your turret. Pulverize and headbutt into turret is super annoying for the leona and will keep her cautious with Zenith blade. His roar also helps sustaining after the little burst if the stun does land. His biggest downside in lane is that he's not a bully, and he will take poke. Leona is generally good with hard engage comps and Alistar helps with peeling off carries and disengaging in teamfights. He's hard to master but definitely worth adding to your support arsenal.
Janna is also a great choice for the reasons you mentioned. Her shield is nice for blocking some of the initial damage while providing time for the adc to get away. Her Howling Gale is also nice for interrupting both Leona and the opposing adc when the Zenith Blade does land. She provides nice harass if you have vision of bush and is good at aiding ganks with her slow and knockup. Her biggest downside in lane is she's squishy and if you do get caught and your shield is down you're kinda screwed. In the later game her Monsoon, movement speed boost and gale provide great disengage for the hard engage of Leona team comps.
Taric ..I hate to add taric to any list but he's good against Leona. His stun provides a great way to keep the opposing adc from doing anything when Zenith Blade lands. His heal provides good sustain after the initial burst. His shatter has a good armor reduction for Leona as well. His biggest downside in lane is that he's melee and aside from throwing out stuns he's not much of a bully. His biggest downside late game is he's useless(I hate taric as support so take the last sentence knowing I'm biased). Taric is great if your team is a catch comp but if its not he kinda just stands around shattering and throwing out heals/stuns in team fights.
Not as common but with a high enough skill I think would be pretty fun
Nami doesn't sound like someone you'd want to pick against a Leona, but give me a chance to explain. You will always be able to land aqua prisons on Leona if she zenith blades! Your ebb and flow onto the adc will most likely bounce to slow either Leona or the opposing adc while healing and increasing the movement speed of your adc. And your blessing will provide a nice bit of extra magic damage to hit Leona as she's up in the air/running away. Her downside in lane is that she is probably the squishiest support, and she uses alot of mana. In team fights she provides great disengage for the heavy engage with her wave and prison. The movement speed increases from her spells and the bonus damage from blessing will make your adc extra potent! It may require alot more skill but she can be a good support vs a Leona.
Soraka is again not great sounding but hold your judgment! Again this another match that requires a bit more skill but will frustrate your opponents. As Leona is Zenith blading in, land your infuse on her, silencing her and stopping the impending stun. Soraka's passive and blessing make recovering from a landed stun easier, as she heals for more on lower health targets. Her bananas provide some nice harass while you're laning so spellthief will provide some extra income. Her global is always great if you're not sure how great your other lanes will be doing. Her biggest weakness in lane is her squishness and lack of engage. This will mean your lane will be more passive and most likely farming near turret, but this will frustrate the Leona cause she cant do anything. In teamfights another downside is she's only good for silencing and healing. Her ult heals are great if your against a pick comp or blessing if someone gets hit with some initial burst. Overall this would be more of a fun comp maybe with an Urgot vs a Leona lane.
Another great alternative to a Leona opponent is just avoid her. Leona becomes pretty useless in 2v1 situations. They can either rotate to counter costing them farm, or deal with it. This requires a bit of teamwork (solo q its hard to make this work), but a lane swap is a great counter to a Leona lane.
I may add more later if I think of any other fun, uncommon supports.