I agree about making positive experiences with children in small steps as described above with the boiled chicken.
Since you don't know any children near you, to get this done, my suggestion (might be a little out there but) is to consider taskrabbit.com
If your city is covered by task rabbit, you can place a task and put a price (say $3 for 3 visits) and write a task title description saying something along the lines of: "Introduce child to my Yorkie." I'd imagine many people would love to be introduced to your adorable furbaby! Task Rabbit bidders are background checked and payment goes through the website. You can choose a public location to meet for safety precautions. -Please note that I am not sponsored by or related to the website in any way and I am not endorsing them. Just making you aware of this possibly viable option.
People there are employed in a contractor basis and there is a point system and rating system so you see the history of the person. You can also make your task one where people bid their own price so you can choose your helper from their profile description or personal narrative submitted with bid.
HTH