You can make a swirl bread or a sugar-studded bread, by adding sugar in chunks. Or soak in syrup after the fact. Or add toppings.
From your question, it sounds like you're worried about the sugar being evenly distributed or the dough being overworked. This might be the case, though Carlton's answer does seem like a viable option if you really want a well-mixed sweetness. However, it doesn't have to be evenly sweetened to be sweet, or tasty, or well received.
One alternative is to use rough lumps of sugar - broken sugar cubes, rough sugar crystals or broken candy, pearl sugar (from which the idea actually came, though it may not be as easy to find). It would take very little shaping to fold them into the dough, so it should not be overworked. The sugar won't be evenly mixed, but it will be a feature, not a problem - the overall effect will be sweet and the textural differences in the sliced bread visually appealing, and the bursts of sweetness will be expected, not a surprise - like suikerbrod. You could even add in some visual effect, perhaps by sprinkling some extra spice that will work with the other flavors, or bits of fruit, or colored sprinkles or something, when the sugar is added.
Another option would be to use a syrup after the bread is baked. You would poke a skewer through the bread in a few places, and drizzle the right amount of sugar, in syrup form, on top of the loaf slowly (with plenty of time to soak in rather than run off). Again, you could optionally add other flavorings into the syrup, though it is not required. This option is used in cakes, to help keep them moist and sweet - a sweet bread, especially if a quick-bread, should find the results reasonable. If there's sugar syrup that doesn't want to soak in, or you feel it would get the bread too wet, you could make a glaze of the rest. Again, it would be sweeter than the rest of the loaf, but that would be expected of a glazed bread.
Another option would be to make some sort of topping to add the sweetness to your bread after it's sliced. The dead-easy option used on all kinds of bread would be jam (or other preserves), this is an easy sweetening option. You could make a glaze (or use aforementioned syrup in individual portions rather than the whole loaf), or else top with whipped cream or caramel or sprinkles, or use to make a layer desert, or toast and spread with butter and sprinkle sugar on top (serve warm), or any number of other alternatives. Again, it may be possible to come up with flavor pairings that work well with your bread's existing flavors or are somewhat neutrally flavored.
You might be able to simply fold the sugar in as you (and Carlton) suggest, depending on where in the process the bread is. But even if that is the best option, I wanted to point out other options are available in case someone should find them useful or inspiring, or came to the problem from a different context.