Here's the big problem with Diana in the jungle...
Mana. She is quite dependent upon blue. Although she would work quite well with a mid who doesn't require blue. (Morde, Akali, Kennen, etc.)
To be fair, I can start at red and it will be a FASTER path than starting at blue. If you start at Blue, you will end your route about 7-8 seconds slower than if you started at red. Wraiths > Red > Double Golems > Wraiths > Wolves > Blue is her fastest route. She has the mana to make it through the route just fine. You only need blue once for her to get going as well. Once you get at LEAST Catalyst, you're set to give mid lane your blue.
What do you build when you jungle her?
It REALLY depends on my own and the enemies teams, but if I had to give core items. RoA, Rylia's, and Sheen.
1. Mercury Treads/Sorcerer's Shoes
2. Rod of Ages
4. Zhonya's Hourglass/Abyssal Scepter
5. Trinity Force/Lich Bane
6. Rabadon's Deathcap/Frozen Heart/Guardian Angel
I used to build Hextech Revolver on her, but I felt that it wasn't that useful on her even when built into Will of the Ancients. And as for Hextech Gunblade, do not buy it. Diana would only get use out of half of it, she does not need or really even use attack damage.
I mean, everything in there should be self explanatory. I really like the idea of Trinity Force on her ahead of Lich Bane simply because it gives her EVERYTHING she needs. Sheen is the more crucial buy because it gives Diana a little more mana allowing her to get out of her mana's early game weaknesses faster, not to mention that sweet proc effect.
Zeal would seem odd until you really thought about it. The faster she attacks, the more times her passives go off, this gives her the ability to continue her burst faster and longer. She can easily stand toe-to-toe auto attacking for good burst damage. It's a nice little touch to Diana, but I love the effect.
Phage, the 2nd most viable item, IMO. If you dislike Trinity Force, build that Lich Bane and use this for Frozen Mallet. HP? Attack Damage? A slow? Not much more you can ask for, for someone who needs to stay on a target. Frozen Mallet only puts these traits to the next level allowing you to truly prevent your opponent from escaping.
I really enjoy these three items as they can allow you to decide how you play Diana, but it will just all come down to playstyle. Hopefully we'll see which can be more viable than the other.