I wouldn't call this "sweet" per se - to me this is the type I grew up with and the one most people would find in their deli case at the supermarket. But in the South, if something is not sour, it is sweet. Example: if you asked for "sweet milk" people would know you didn't want buttermilk.
This recipe is from Saveur magazine and was developed by Rick Bayless whose parents owned and ran a barbecue restaurant in Oklahoma City. It is so easy it can be made in 15 minutes.
1/2 medium head green cabbage, cored and very thinly sliced (about 8 cups)
1 small red pepper, roasted, peeled, seeded and chopped into 1/4” pieces
3 ribs celery, cut into ¼” dice
3/4 cup mayonnaise
1 tbsp sugar
1. Put cabbage, pepper, celery, mayonnaise, sugar and 1 tsp salt into a large bowl and toss well.
2. Adjust seasonings with more salt, if you like.
3. Cover bowl with plastic wrap and refrigerate until ready to serve. The flavor and texture are best when slaw is made an hour or two before serving.