Diana is a risky choice in the jungle, and in general, in my opinion. She's definitely best in the jungle where she can get almost entirely free levels without getting much harass from enemy champions. Counter jungling happens, but it's better than getting nuked every time you go in for 25g and having very little answer to it until 6.
Anyway, she kind of relies on her lanes to not lose or at least not feed until she's level 6. In that sense, she's a lot like Warwick. What's different here is her damage and outplay potential.
I play Diana exclusively in the jungle. If Diana gets banned, I'll play something else to get by, but I won't be able to even remotely carry. That being said, I think I can help a bit by saying that ganking doesn't always mean getting a kill. Just showing up in lane and landing a Q is generally enough to give your lanes some room to breathe. Pre-6, you really wanna just farm the best that you can. If you're top side pre-6 and they ping for help bot, make you way down there but ward wherever you think you might get counter-jungled if at all possible. i.e. Red buff. Post 6, farm squishy champions. After an Abyssal Scepter, you'll have no problem nuking an ADC or mid laner 1v1 and before that you'll still be able to do significant damage to at least get an assist or pull off a "kill secure." ;)
Basically, you don't have to get a kill in every gank. Just take pressure off. If it doesn't work out, move on to your next camp. That enemy laner now at least knows you're watching.