It received a nerf in the latest faq, since the armor that forced to reroll wound rolls now has to be used and is a light armor, but that's far from saying that they are weak. After all rerolling wound rolls of 2 is not that terrible, like when a cannon shoots at it.
The fact is the prince could easily take the armour of meteoric iron, the relic of the desert sun and a talisman (for s grand total of 75 pts) and always have a 5+/5++/5+++, or the armor of destiny (with a shield) plus the relic for a 4+/4++/5+++. So even with a cannon, in the first case it has a 70% chance of saving the shot, in the second case i think it's around 66%.
Now i have surprisingly noted that my cannons are able to last most of the game, often being some of the last units to die if i lose, but that's because generally there are fewer snd fewer targets starting from turn 2. Ideally the khemri olayer will have the dragon engaged somewhere on turn 2, possible free again if he wins in his combat phase, so usually i manage to get at best 2-3 turns of cannon shooting on them (so let's say 6 shots, and I'm being generous). Generally at least one is a mishap, so let's say 5 shots, with 2/3 of them being saved that's like, with the average of 3 wounds inflicted is like 5 wounds out of 9. And getting three full turns of shooting vs the dragon is a big if.
Combat resolution might be a solution against other dragons, but the khemris are undead so they do not flee, they lose additional wounds and give ground. You might try a big unit (like 24) of spearman with bsb, griffon banner and war banner. That's cr8 for starters, you could use a detachement for an additional 1 but the dragon might just charge it so that's not good. You throw a challenge with the champion, he has to accepts with the dragon, so at best he will inflict 5 wounds and lose the fight by 2. He loses no wounds in this case but he will Give Ground. You restrain your guys (they are veterans so you should make it) and in your turn you will try and shoot the hell out of it.
With a little bit of magical support (like a couple of demonology spells, or a 5+ wards, wither from battle magic of from elementalism) you coule maybe even inflict a wound or two, so it might even retreat and lose one or two wounds. If you want to do this twice you are going to need an additional character. Just because he might be a witch hunter that chooses undead, in the off chance the other player does not put the relic on the dragon.
Now the dragon ha 5 attacks, d6 stomp so vs veterans that you are using (otherwise no magic banner on them) it hits on 4s, then you have 3.5 hits, plus stomps that's 7 hits, or a little less than 5 dead state troopers. The rest is in the hands of the rider, but with a little bit of magical support