I am looking for a coffee type that is naturally sweet, like sugar snap peas. So there is no need to add sugar, when I drink it.
This question is probably best answered in two directions:
If you feel the need to add sugar to your coffee, it may simply be that the coffee that you are drinking is not very good. Sugar makes a lot of things taste better in addition to the sweetness that it adds. There are many ways to improve the quality of your coffee, like buying better and fresher beans, grinding right before brewing instead of buying pre-ground coffee, etc. Whether any of that is feasible depends on your coffee drinking circumstances - e.g., if you need to use your office's drip coffee machine with the coffee bought by the kitchen management, there is not a lot that you can do.
If you want to add sweetness because you like it sweet, but you still want to avoid adding sugar for some reason, you can try the following:
There are a couple of coffee bean types that have a slightly sweet flavour. For example, I have a some "Starbucks 2015 Christmas Blend Espresso" here, which is described by the producer by "Cedar and herbal spiciness with an intense caramelly sweetness". When using the beans in a pump-driven espresso machine, the espresso indeed has some sweetness. But don't expect too much. Coffee is natually low-calorie, which means that there can only be a little bit of sweetness. There are some coffee types that are naturally sweeter than others. According to a book that I have, lightly roasted Arabica Bourbon coffee beans should have a "fine sweetness". Panama Volcan Baru Coffee is also listed as particularly sweet. Against, don't expect too much - "particularly sweet" means in comparison to other beans!
In case you prefer to drink your coffee with milk, you may want to switch to lactose-free milk. In that type of milk, the lactose has been split into shorter sugar molecules, which makes the milk taste quite sweet without a noticeable change in calories.
There are several coffee varieties that have a "sweeter" taster. Varieties that have a delicate taste like Rhume Sudan, Geisha, Villa Sarchi, Montecristo, Bourbon, Maragogype will produce a sweeter cup when you apply a softer extraction (like a V60), and you use a light roast and natural or whiney processing. However, as stated on another answer, coffee has very low calories and contains very few sugars, beside trace leftovers from the fruit during processing. So don't expect a strong sweet taster, but rather a very subtle reminder of sweetness.
Plants growing at lower temperatures have a better chance to accumulate sugar in the cherry. As a rule of thumb, temperature lowers as elevation increases but at higher altitudes other flavour qualities are lost. Your best bet is finding places where altitude is not too high but climate conditions provide cooler climates. In Colombia, coffees from Nariño; Filandia, Risaralda or Oiba, Santander tend to be very sweet.
A few considerations when choosing a 'sweet' coffee..
I saw posted that lower elevation equals more sugar. Lower elevation also typically signifies higher caffeine which is very bitter.
Look for light roasts with mild acidity. Why light roasts? Coffee beans coloration comes from Maillard reactions, a key component of which is sugar caramelization. While in your mind, caramel is sweet, raw sugar (sucrose for instance) is significantly more sweet than caramelized sugar.
Why low acidity? While acidity isn't bad in a coffee, I feel like if you are trying to optimize sweetness, acidity detracts from perceived sweetness.
It's really difficult to say what origin is most sweet, but it may be a better approach to say what origins have flavor components that might help add to a perceived sweetness. For me, I like a good Guatemalan or Ethiopian for a clean, brisk sweet cup of coffee.
One other note.. Espresso roasts 'should' be optimized to minimize acidity and bitterness while maintaining as much sweetness as possible. You may find some espresso beans that will fit the bill for sweetness, but I still think you can find more sweet coffees at lower roast levels.
It depends on what kind of "sweetness" you're looking for. I don't think there are any naturally flavored coffees that will give you a white sugar kinda sweet, at least nothing that I have come across yet.
But I think that a lot of the Ethiopian coffees that are naturally processed give a really sweet taste. More like berries(blueberries and strawberries.)