I had a ridiculously enormous piece of carrot cake while I was in Dallas, which reminded me about this recipe that I haven't made in many years. I can't take credit for the recipe itself, but I'll give you the link and my advice for getting it to turn out right based on past experience and having made it last night.
It's called Fourteen K Carrot Cake and the thing about it that makes it way less trouble than 99% of the carrot cake recipes in the world is that it doesn't contain grated carrots. Instead, you make it with baby food carrots and you get the expected carrot-y texture from coconut and crushed pineapple.
It also gets points for not even mentioning the one thing I don't like about most carrot cakes: raisins. Bleh.
The one place where the recipe steers you wrong is the baking time. It says 40 minutes, but it's really a good 55 minutes if not an hour. At 40 minutes, the center is still all woogy when you give the pan a poke. Yes, woogy is a baking term. I don't know why you've never heard it before.
I let the cake cool overnight and then I made a batch of this cream cheese frosting. I used a food processor to mix the ingredients, which I highly recommend. I even more strongly recommend letting the butter soften as the recipe instructs because otherwise you'll be picking out big chunks of unblended butter while you're applying the frosting to the cake (heh).
As you can see from my blurry camera phone photo, it's a thick cake that rises almost to the upper edge of the pan. My colleagues worked on it all day long and didn't even eat it all.
So the bottom line is that this cake absolutely rocks and you should make it. You won't be sorry.