How can I get a small bookcase to put under my kitchen counter?

What is the size of bookcase you are looking for? Have you tried a local thrift store? Why not put in open shelving instead of a bookcase? That way you could adjust the height of each shelf to your liking (6 inch shelf for spices, 12 inch shelf for cookbooks, 2 foot shelf for hanging pots, etc.).

I would look at goodwill or thrift stores and also Target, Walmart and some of those stores sell inexpensive and all size book cases.

https://www.pinterest.com/pin/245024035953874413/

Check out places like Salvation Army, Goodwill, used furniture places, even garage sales if the are going on in your area at this time of year. The Sauder brand has many different bookcases, check them out online or in stores that carry them. Most stores, even Walmart, Kmart and home improvement stores may also carry them.

I would look on Craigs List, Nextdoor and FB Market Place and put an "ISO" add out there and tell them what your dimensions are. Since it will be cheap, then you can put your time into finishing it to match your cabinets.

Given that bookcases are never deeper than 11-12" and kitchen base cabinets are 24" deep, are you expecting to find a bookcase 24" deep?

If so, you'll need to contract with someone locally to build you this kind of cabinet. Or...

If you want to do this: Buy a shell of a base cabinet drilled for adjustable shelves and the shelves, with no toe kick. Then put a 2x2 (1.5x1.5") plinth base on it.

It's not going to be cheap, but it will be tough and 24" deep, and widths from 15"-42", if deep is what you want.

I would thrift for these items. You can cut them down to suit your needs.