My core build: 
Note that I don't say "secret OP" because Leona's truly not overpowered in the jungle (Sejuani does better damage and has better clear speed). I just know how to make her work through lots of practice, as well as trial & error.
But seriously, try it out sometime. You'll find it fun.
Deep Terror Nami2 votesHow was your initial clear?
darkdill1 votesLeona's initial clears are always slow, but that's to be expected and, if anything, is an intentional weakness. If Leona could clear well, she'd be OP as a jungler.
What I do is go Gromp, Wolves, Red, and then look for ganks. You can only go Gromp > Blue > Red if you have Bard plant some shrines for you, or if you have a Soraka leashing for you (otherwise you'll take too much damage and could die to Red). Don't go Krugs first, even if you're on Blue side, because Leona's poor attack speed doesn't work well with that buff. Poison Armor is much more helpful.
When you finish the Red camp, if you can't find anything to gank, roam around and kill a Crab or two, letting health regeneration pick you back up over time. I try not to go back to base until I have at least 1k gold so I can at least get Bami's Cinder. That will let you clear camps much more easily.
Hard4Hamsters1 votesI've done it. It's really slow. I do a back after the first 3 camps I clear. (Gromp, Blue, Wolves/Wraiths..woops "Raptors") For Trailblazer. It is nearly a must on her. Then you hit up Red buff look for a gank mid. If not, go to Scuttles and take that real quick..ish and look for a gank bot or mid. If no ganks are really that possible (both lanes pushed into enemy/enemy playing far back). Ward up Tribush or enemy jungle and then go down to Krugs and depending on the situation, go for a full clear of the jungle. You will probably want to back unless a gank/countergank opportunity arises.
Grab Bami's Cinder/Cinderhulk if you have the gold, boots, some wards (just work towards Cinderhulk and getting your boots but if you have 350 gold after Bami's/Cinderhulk, you might opt for wards and potions over getting your boots. Next you can give away Blue buff to your midlaner if he needs it, as you have Bami's and Ranger's to help with clears without expending considerable mana. You should be looking to gank a LOT as Leona as you have good CC and should use it, and your passive works with allies really well. But if you don't really have much opportunity, you should focus on vision so you can spot the enemy jungler (not to fight him 1v1) but to find out where he is to set up counter ganks and give your laners good information on whether or not to stay back. Clears should speed up by now so play pretty close to how you would play Sejuani, looking for ganks whenever your Ult is up. You are really strong in teamfights and should work to be a peeling tank for your carries during fights.
Buildwise: Get CDR and health. Aura items are really good on her so 
and are near must haves. 
and 
are great items (Righteous Glory is more for snowballing) Randuin's is more defensive. Other options are
and choice of boots. I don' agree with Ohmwrecker, it allows you to be really aggressive, but has a real lack of utility in many situations. If you like it though, you do you.
Anyway, she's pretty strong as a jungler if you can get past the first 8 minutes of the game; this means don't pick her into 
:P.
Runes: AS Marks, HP/lvl seals, CDR and MR/lvl glyphs, and Armor Quints. Masteries: 9/21/0, 6/24/0, or 0/21/9 (6/24/0 grab CDR, Extra 2% take 1%, and Expose Weakness in Offense; 9/21/0 I grab AD instead of AP, as your scaling is kinda bad and AD helps you in clears a little more).
Suggestions are welcome. Try it out though. It's actually kinda fun playing. Peace.
darkdill1 votesOhmwrecker has saved my ass several times with the Point Runner effect. 30% bonus movement speed near turrets really helps Leona's lackluster speed.
Though yeah, it's not nearly as useful if your team is behind. I kinda wish it had some sort of defensive functionality to its active when used near an allied turret.
Deep Terror Nami1 votesNew: Ohmwrecker - When used on allied turrets, overcharges them to shoot twice as fast or (for tier 2 turret) immediately grant full shield to allies in range.
khorney1 votesIt's not as bad as it sounds max w but you need movement speed quins and mastery tree and ad . I'm in the processs of doing this
darkdill1 votesI've done just fine with a pure tank setup. HP regen quints are actually quite handy for letting you stay out in combat for longer.
FantasySniper1 votesI did Leona jung a long time ago. I tried it again later down the line with new and improved Cinderhulk, but it just sort of fell flat.
In comparison to Sejuani, you're getting harder CC and somewhat more tankiness in return for less damage and overall less reliability. It works if you can get a carry on your team to go ham when you engage, but otherwise you're so lacking in damage that you won't be much more than a peeler. It's fun to do, and snowballs hard once it gets going, but it's overall pretty difficult to pull off :/
darkdill3 votesLeona's got one extra advantage over Sejuani: her ultimate recharges faster. This means Leona can gank at full power a lot more frequently than Sejuani can.