There are many possible ways to automate 'API Calls', The best automation tools would be JMeter for functional tests and frisby.js for testing API endpoints.
frisby.js is a REST API testing framework built on node.js
The 'Apache JMeter' application, is an open source software, a 100% pure 'Java application' designed to load test functional behavior and measure performance. It was originally designed for testing Web Applications but has since expanded to other test functions.
However, JMeter API's can be used in java program. here is a JMeter API Documentation for more information on JMeter API, Also Please refer to this threadthread, to understand how to run an entire test plan programmatically from or within a Java program.
It would be best to create a test plan .JMX file using JMeter GUI and run it in JMeter 'non-GUI' mode.
For creating a test plan in JMeter GUI. you could find more information in this thread. Well this tutorial was very helpful to me for learning to create 'JMeter scripts'.
If you have a basic understanding of javascript, you can try 'frisby.js' referring to this tutorial. I believe both these tools are perfect for API coverage.