Try to find a bike with a road triple on it. I believe Shimano still makes a triple in the Tiagra line, maybe some others. That crank will probably be a 50-40-30 or something like that. With that, you can go as low in back as a 32 probably with current road rear derailleurs. Or, depending on compatability with the shifters, you could go with a full on mountain bike cassette in back with a mountain bike derailleur. That's what I put on my wife's road bike with 9 speed Tiagra triple in front. Her lowest gear is 30 X 32 (or 34, can't remember) with a Deore rear derailleur. Works great.

Getting more fussy, you could consider putting a mountain bike triple crank on a road bike and get a small chain ring in the 24-28 tooth range.

Basically, if you're willing to buy and install parts (which really is pretty simple), you can put mountain bike crank and cassette on a road bike and get as low as 24(front) X 34 (rear). THAT's a granny gear!

You can play the used parts game on ebay and reduce the net cost by selling the stuff you take off. And, lower level MTB stuff will work just fine and doesn't cost an arm and a leg.

In my experience, a Shimano road front shifter and derailleur shifts on a mountain bike crank just fine. It's the rear indexing you have to make sure will work OK. I'm not up to date on what mountain bike rear derailleurs Shimano 10 speed road shifters will shift. With 9 speed, they'd shift any 8 or 9 speed MTB RD, so it was a very easy conversion.