For undergeared tanks there's not really any answer. If you're at the point where you're spamming heals and it's still not enough, even with your gear being solid, then you have to accept that there's nothing you can do. Just get them to pull smaller packs, and suggest upgrading their gear as soon as they leave the dungeon.

For selfish tanks, I assume you mean tanks that don't bother with cooldowns and just expect the healers to do more work? If so, again, all you can really do is talk to them and try to get them to mitigate a little more. If you get hit with a "You don't pay my sub", then at least you tried, but you're not the jerk in this case.

For jittery tanks do you mean tanks that aren't all that confident and are maybe not using cooldowns optimally? In cases like that, again, explaining that dumping all of your cooldowns at once instead of spreading them out isn't ideal, or using your big 30% ones when there's only 2 enemies left from a 7-mob pull is a waste. The problem I found with jittery tanks, however, is they take the "You can use fewer cooldowns" and dial it to 11 and accidentally become selfish by overcompensating.

All in, it's mostly a communication issue. If you're absolutely sure that your gear is up to speed and you're outputting as much healing as you can, then the only issue lies with the party. Especially at your current level, which I assume isn't much higher than the 30 White Mage. For any general tips at that level I'd say try and keep Regen on the tank while you're fighting if you can spare a cast on a slower spell, as that ticks in the background for more healing than Cure 2 over its duration. And try and save Presence of Mind for moments when the tank should be out of cooldowns, but still taking heavy hits. Cure is more MP efficient than Cure 2, if running dry on MP is the issue, so while Cure 2 is a bigger heal bomb and is real good for keeping tanks topped between casts of Stone, it's a massive drain on your own resources if you need to go ham with it. You get a free-proc trait for Cure that lets you cast Cure 2 for free on a 15% chance which really helps with MP management. Also you should be using Lucid Dreaming from your role skills early and often. Don't keep it until you're already out of MP: much like tanks and their Rampart it's better used to prevent problems, not solve them. So if you use it at about 7000 MP it will tick in the background and keep you well stocked.

Eventually you'll get more tools to deal with it, but for now more than later, dungeons are very dependent on the party: you can't heal a tank wearing tissue paper, likewise a perfect tank will still have issues if their healer runs dry after 5 seconds. And it's all well and good both being ideal, but it won't matter if the DPS don't kill the enemies quickly enough and everyone runs out of cooldowns and the like. This last point is also something to take into account: if you're doing Tam-Tara or the like and the tank pulls wall to wall, that's fine if you have, say, a Red Mage and a Machinist, since they have great AoE attacks at that level and can kill everything really quickly. But if you're with a lancer and a rogue they can only kill enemies one at a time so if they pull a massive group then they have to deal with the massive group for longer.

tl;dr- communication and managing your MP.