Yes, thank you @roadscape! I figured it out!

I was able to change <code>posting</code> key with the <code>cli_wallet</code> command:

<code>update_account_auth_key account_name posting STM884pLqzhwjpS7MotzfH2iXppnoBtaXQvN8uLBt1t99eShvKgCK 1 true</code>

The same command used to remove previouse <code>posting</code> key from the account - you have setup <code>weight</code> to that key to zero:

<code>update_account_auth_key account_name posting STM6xDB2hRiH8rFT75oidwmk4hVKyvRbyrfHtJpmMKewEVDBkzG58 0 true</code>
This is required to be able to login to steemit.com site with new <code>posting</code> key. You will not able to login on steemit.com if you have more then one <code>posting</code> keys.

Please note: regarding <a href="https://github.com/steemit/steem/issues/172">Issue 172</a> if someone uses a string other than owner, active, or posting for the authority type argument of the update_account_auth_key CLI command, it will silently treat the authority type as if it was owner.

To change <code>memo</code> key use <code>update_account_memo_key</code> instead.