The best solution I could find for this problem is to specify private key file in ansible.cfg (I usually keep it in the same folder as a playbook):
[defaults]
inventory=ec2.py
vault_password_file = ~/.vault_pass.txt
host_key_checking = False
private_key_file = /Users/eric/.ssh/secret_key_rsa
Though, it still sets private key globally for all hosts in playbook.
Note: You have to specify full path to the key file - ~user/.ssh/some_key_rsa silently ignored.