Just sent Brian at Coinbase a note about this. I'd use the feature constantly if they added it. It could be as simple as selecting a funding source when you send; your wallet or an option to purchase what you're sending.
I emailed them about this idea a few weeks ago and they replied with this:
"Thanks for your feedback - that's a great idea! I'll pass this on to the team so we can look into implementing that!"
Trouble is it's not anonymous. If you could find a way to do that anonymously, that would be amazing.
Just find a friendly localbitcoins seller. Hand him cash once a week while you're at your favorite coffee shop.