How can I setup two iCloud Keychains? I want to replicate my Keychain setup for OS X in iCloud Keychain, to have passwords sync between iOS and OS X devices.

The way I set it up was following this article. The idea is having the default login Keychain for all Wi-Fi and system passwords that remains unlocked after login, and a separate Keychain for website passwords that is kept locked and requires a password in order to access the passwords when needed.

I would like to access these website passwords from my iOS devices in this same way, only when I set up iCloud Keychain, the login Keychain automatically became the iCloud Keychain.

Is there anyway to have to separate iCloud Keychains syncing between my devices?

Alternatively, is there any other way to make the passwords in my secondary Keychain available in iOS?
There's no way to have more than a single iCloud Keychain I'm afraid. Other Keychains you create locally on your Mac are only for use on that Mac.

Until Apple allows Keychain Management on iOS from Settings you're out of luck. If you're interested to know how iCloud Keychain works, see here: https://support.apple.com/en-au/HT204085