To get the ecommerce conversion rate with Google Analytics API, you can use the metric ga:transactionsPerVisit or ga:transactionsPerSession depending of API version you are using.
Enjoy ! 🙂
International SEO Consultant (Freelance)
Founder of Kelogs, a SaaS SEO Crawler & Log Analyzer
Over 15 years of SEO experience
Read more about me, myself and I.