It is relatively easy to turn an STM32F103C8T6 (BluePill) into an STLink programmer. All that is needed is a copy of the STLink firmware and a means to flash it. Do a search for STLinkV2.J16.S4 and download it. Flash that binary file into the STM32F103C8T6.
The new STM32F103C8T6 STLink can then be upgraded to the latest firmware version from https://www.st.com.
Here is the wiring diagram on how to connect the new STM32F103C8T6 STLink programmer to another STM32F103C8T6 to program it:
Download the Fritzing Diagram from HERE. Actually, the capacitor and 4k7 resistors on the right side of the diagram are not needed (it works fine without them).