I'm not paleo though I am friends with people who are and I do keep to natural, unprocessed foods as well as try to avoid carbs/gluten. I'm the weird person that can leave cookies and cakes sitting out and not obsess over them or feel like I need to eat them. It's not that I don't like the stuff, since I love ice cream and cookies, but that my sweetness tolerance just seems to be lower than other people's. I'm Chinese-American and one thing that I've noticed is that Chinese sweets tend to be much much less sweet than sweets from other cultures. This might be why I can leave sweet things alone after a couple of bites and why I always need water or plain tea afterwards to wash the sweet out of my mouth.
My advice is to eat fruit instead of sweets, especially fresh fruit and not the dried stuff that's essentially concentrated sugar. Try tropical fruits like mango, lychee, papaya, etc. which I find tend to be sweeter and more effective in quelling sweet cravings than regular apples and pears. Grapes are wonderful. Although fresh fruit might not hit the same sweet spot, pun not intended, the sugar they contain will elicit the same chemical reactions and they'll fill you up faster (yay fiber). Roasted vegetables like carrots, yams, and beets are also full of natural sugar and are delicious in addition to being healthy and paleo-friendly. Reading other posts on fruit and the avoidance of fruit, I have to say that in the end fruits are better than sweets but veg are the best, if you must have sweet + nutrition.
The problem with paleo as with other diets is that people try to go cold turkey and hate themselves if they relapse. I think that some people might be able to strip their diet of everything bad all at once, but tapering and removing one food type at a time seems like a better idea. Admittedly, it takes longer but your body has time to adjust to every change so you're not left with withdrawal pains/cravings. You essentially have to treat your sugar intake like an addiction. Your body wants sugar because it's been programmed that way (which means that it rewards the intake of sugar with feel-good endorphins) and you've fed that cycle of urge-feed-reward for so long (until you went paleo) that your body will crave sugar when your body chemicals are out of wack. As with other substance addictions, the important part is reducing your reliance on the/your intake substance before finally eliminating any intake.
As PaleoGran said, making sure you're sleeping and exercising enough, drinking enough water, and that you have a structured food plan that doesn't allow for sugar to creep in is essential. Make sure you're full because I've found that when I'm hungry, that's when the crap cravings starts to get to me most. Eat other things that you enjoy or do things that get your endorphins going. In the end, it's all about harm reduction. Replace bad things (sugar) with less bad things (red meat).