Where are you located? You may ask your Dr about official disposal means where you are.
However, after the syringes are used you put the top back on them, and place them in a sturdy plastic bottle with lid when the bottle is full tape the cap shut.
I have read in the past of a small electric machine that can actually melt the metal part of the syringes and turn them into small balls of metal that will not be dangerous to anyone. You may also wish to look whether such machine is available.
My doctor disposes my pen needles, lancets, and strips for me. I purchase a Sharps container from Walmart for about $7. This container can also hold syringes.
One of the doctor's nurses also suggested using a clear 2 liter soda bottle to hold the waste.
So I would suggest asking your primary care doctor or endocrinologist if they would dispose of the syringes and what method they want you to use.
I hope this helps.