How to get rid of old rosaries properly?
Give them to your priest and let him do it.
You can re-sell them to other people who will still be using or give them out as donations. If they are broken, some people are also known to recreate and make something new out of them.
Throw them away. Unless you can read about them and their purpose in the Bible then mean nothing to Christians.
Rosaries are not sacred objects and can be disposed of like anything else.