The way OP answered his own question is one way to go about it.
The Windows Credential Store project was discontinued in 2015. Its original author suggests to use Git Credential Manager for Windows, maintained by Microsoft. Their installer is focused on Git for Windows, however the program itself works well with Cygwin, you just have to install it manually.
Go the GCMW’s latest release, download the zip file (not the installer), extract its contents (only .dll and .exe files are needed) to C:\cygwin\usr\libexec\git-core\ for 32-bit Cygwin, or C:\cygwin64\usr\libexec\git-core\ for 64-bit Cygwin. Reference
To get git to use GCMW, execute: git config --global credential.helper manager
To get GUI prompts for credentials, execute: git config --global credential.modalprompt true
If you want this to be a per-repository setting, remove the --global option.