Window balances
Hello there. This looks like a 15-177 Pivot Shoe, which uses Series 152 Coil Balances, sold separately. For the coil spring, you need to select a spring weight, which indicates the weight the individual coil spring can support. There is sometimes a stamp on the old coil tape, usually near the tongue, that indicates this. If there is none, give me the exact weight of the window sash that these coil balances support, and I can work out what you need.
See our 15-143, 15-144, and 15-145 components. This is a newer design, but will work as well as your old support system. These parts simply 'sandwich' around the Series 152 spring. Let me know what you think.