In a medium saucepan, off heat, mix together sugar, salt and cornstarch. Gradually whisk in coconutmilk, mixing until ingredients are dissolved. Whisk in egg yolks.
Cook over medium heat, whisking constantly until you see it barely begin to bubble. Reduce heat to low and continue to whisk and cook for 1 minute, until thickened a little. Remove from heat. Stir in vanilla.
In a food processor or blender, puree the avocado and lime juice together. Pour the coconut mixture into processor or blender and puree until completely combined and smooth. Taste and add sweetener if needed.
Divide mixture among popsicle molds. Chill in refrigerator for one hour and then insert the popsicle sticks, then place in freezer for at least 4 hours, until frozen solid.
Run mold under warm water to release pudding pops, then enjoy!! (makes about 8-10 popsicles)