What are the solutions in C2 to create an IAP system for web browser games?
Develop games in your browser. Powerful, performant & highly capable.
There are many threads regarding this, try running a search. Have you checked in the stickied FAQ thread? - Specifically in the section "Monetizing".
EDIT: My apologies, missed the web browser game part >< See below.
Short answer: There's none, short of finding a payment handling service that has an api, and writing a plug.