Facing Leona is problematic. Remember, once her rotation is down she isn't threatening anymore, in fact she has a chunk of bonus AR/MR at that point. In fact, if the Leona is good, she probably has enough regen to shrug it off. Poking down her AD carry is a good idea - but as soon as you engage the cards are in Leona's hand, so don't do that until you're absolutely sure.
This is how I think Leona fares against some random supports I have matchup experience against.
Soraka - problematic MU. You need to burst down Soraka or else you're not going to do much. Infuse is free against any sort of approach of Leona's save for Solar Flare sniping. Her sustain means she'll usually win trades, and the burst heal counters your attempts at killing but she's weaker early so abuse her around levels 2 to 4. Consider bringing Ignite.
Sona - like Soraka, minus all the tools of Soraka that make killing things problematic. She has considerable poke and can also sustain, but Sona is pretty free before 6, can be sniped rather easily even afterwards, is really squishy, is in Zenith Blade's range if she tries to poke anything and so on. One of Leona's favorite enemies to face. Be mindful of Crescendo and don't underestimate her, though.
Taric - not that much of a problem. Should he dazzle your carry, get on theirs, you're a bigger threat. Then get on Taric when he tries to abscond. He has a heal while you don't, but he loses the offensive game - which is kind of what he's picked for, apart from the auras - so this should be a pretty even matchup. Get some sustain in case you get bedazzled.
Lulu - no heals on either side = this lane is risky. Lulu obviously has superior poke and can prevent you from striking back, but she needs to be careful as well so that she doesn't get pounced on, because no sustain. Bully her as long as Pix is down, bait Pix and then go for it, bully her if she doesn't have enough mana to keep the harassment up. You're going to take a lot of things on your chin anyway, so you should bring the sustain and take care of your ally. If Lulu is teamed up with a good poking carry, though, you will probably regret your choice of support.
Alistar - same deal as with Taric. If he gets on your AD carry, you get on his. Ali can be more dangerous offensively than Taric - he also has more mana costs than you. Abuse that and play a bit more offensively, provided that you can take it and your AD carry backs you up. You absolutely need to respect his CC abilities, he can mess you up hard when you're out of position and he knows it. Obviously, don't try to kill him unless he asks for it.
Blitzcrank - can be tough. Expect the rocket grab, avoid the rocket grab, avoid the rocket grab that comes when you're trying to disengage, ward the bush. Take the fight to him. Unlike most other supports he isn't all burst and no sustained, and he's a tanky little bugger. But his close-up CC is lacking and usually he doesn't really want to grab you. Stay at high health, just in case.
Janna - can be annoying. Free damage if you hit her with a Zenith Blade, though, and also free if Eye of the Storm is down, so get down to baiting that bugger. She doesn't hurt, either - so altogether you like seeing her, although you might not get many kills.
Thresh - has no sustain. Yes, you can't really kill him or his carry and he's dangerous if he manages to engage on people - but no sustain plus plenty of opportunities since he wants to get out and get souls equals not really that big of a threat.
So, generally - Leona really likes it if you have no good GTFO options. Leona dislikes heavy poking comps. Leona dislikes it if the opponent can win the trades she engages, so once she's behind she'll have a bit of a hard time, but that goes the other way as well. Respect Leona from 2/3 - 6, and don't move so predictably that she has an easy time getting you with Sunlight. Taking control of the brushes never hurts. Know her damage - a basic combo from her alone can be around 40%, and with her ally chiming in things will hurt. Know that she deals most of that damage over three seconds and that a lot of it comes from innate and W, both of which allow for counterplay. Know that Solar Flare means that a good Leona can always engage you if she wants to, and that she's scary when she gets her ult as a result. Any lane with Leona in it is a kill lane.