Automatically Show a Form at Bottom of Page or Post

I've done some searching around docs and the support forum, but wondering the best way to automatically show a form at the bottom of {almost}* every page or post? Need to make a "quick contact" form. Want it to show at the bottom, just like an Author Block, or Sharing widget.

I assume it can be hard coded into PHP, but I'd like to avoid that.

*Plus I'd like to have ability to override a given page - like the Contact Us page (don't want to show a quick contact form on the contact page that has a bigger form)

I know it can be easily added with a few strokes via short code, but I've got a few big sites (100s of pages, and can't go back and edit every one)

Is there a 3rd party plugin that can do this? Or any other way?

Thanks,
Blake

Thanks David . . that was quick ;) The PHP solution is what I was afraid of, not completely out of the question but was hoping to avoid.

But the "Merge Tag" thing - I'm sorry, can you expand on what you mean?

Ahh, okay. I thought maybe it was me that was googly-eyed from staring at code all day.

Thanks for the support!