what part would this balance bee

Thanks for reaching out to us. We should be able to help with this. Before I recommend anything, could you show us a photo of the inside of the metal channel where the innerspring connects to the pulley mechanism?

Thank you kindly! My recommendation is the S351-12 or S390-12 channel balances. The difference between the two is the depth of the bottom shoe. You'll have to measure as shown below. I also recommend the 1120 stamp option for your replacements. 

Comparison of the S351 and S390 balance shoes.