I can use API Eth to send and check transactions as API BTC . But it does not seem to support
please help me!
If I understood your post clearly,you want to implement a payment system in ETH where you can send/receive ETH and check the transactions history.Why coinbase? That's a bad choice.
There are many other third party apps which let you do this with minimal lines of code.
Try :
https://www.coinpayments.net/