Our sink has a pop-up drain that doesn't connect with a rod. Haven't installed it yet, but it's a Pfitser push and seal that came with the faucet. You could probably buy them separately...

Here is a link that might be useful: push and seal drain

my sink has a pop up drain as well and is not a vessel sink. It screws in.

We have these installed in our sinks. We've only been using the bathroom for a few weeks, but they work great so far.

Here is a link that might be useful: Pop up drain