Hello Kirk and thank you for posting in our forums!

While we currently do not automate the actual printing of packing slips, you can set Shipping Rules to assign specific packing slip templates to your orders based on Store or other variables. 

By using Shipping Rules in conjunction with the filters on the left side of the orders screen, you could essentially print packings slips with just a couple clicks. The link below explains how to create one of our more popular Shipping Rules:

Assign unique packing slips to orders per store

And this link explains how to easily print packings slips from the Orders screen: How to: Print packing slips for unshipped orders

We certainly welcome you to also post a feature request for Packing Slip automation in our Feature Request forum:

Feature Requests - Productivity: Features, Interface & Settings

This will allow our CEO and Product Team Managers to see your needs first hand.

Thanks and Happy Shipping!