I don’t can much anymore since getting into lacto-fermentation and lowering our family’s consumption of sugar. Rather than jam, I will just use fresh fruit on nut butter sandwiches, or make a quick jam by cooking down the fruit and adding a small amount of honey and storing in the fridge for a week.
If I need to preserve a lot of fruit, I just freeze it. I’ve also made “freezer jams” without any added sugar and using Pomona’s pectin.

Most people are used to preserving with a lot of sugar, but the fact is that you can preserve without much sugar or even none at all, provided you use proper methods.

Here is my favorite resource on how to preserve without sugar http://pickyourown.org/canning_without_sugar.htm

If you want to use sugar, this is a good resource for learning to preserve using honey:
http://real-raw-honey.com/canning-preserving-with-honey

http://www.stevia.com/Stevia_recipe/Berry_Jam/16

http://www.sugarfreestevia.net/sugar-free-jam.html

I believe I’ve done this and it works. But it was awhile ago.