How do I make sugar-free ice cream without a machine?
You could use sugar substitutes but you should take care to use one that is heat stable. 

Sugar Substitute with Stevia as main ingredient can be used but you need to inquire to what ratios you would need to use your specific brand with.

Acesulfame Potassium is heat stable but is 200 times sweeter than regular sugar. The general rule of thumb I was taught is 1 gram per quarter cup of sugar.

Sucralose: Granulated sucralose can be used as an equal-volume substitute for sugar. (Raw sucralose is 600 times sweeter than sugar, so you'd use less, but the granulated form contains fillers to bring it up to the normal volume.) There may be some considerations in making ice cream with this as when using this for baking the baking process is accelerated to a certain degree. Be careful with this one.

Saccharin and Aspartame should be avoided because they are heat sensitive. 

Other more natural sugar substitutes include honey, fruit juice concentrates and refined fructose.