Non relational database for twisted
One of possible solution is using Redis(REmote DIctionary Server). Redis is very fast, powerful and stable key-value storage which is used in many projects. Stackoverflow also uses redis;).
I've recently start using redis in my current project for creating user's ratings. My personal opinion: redis is very simple, very fast and stable. It also has a pretty command line client, I like it.
On website I use synchronous redis package. Server uses twisted and requires asynchronous approach. Fortunately, there is third-party module txredis, which allows easily to interact with redis database using twisted. I didn't have any problems with it. However, txredis doesn't have a connection pool, but it's not a problem to implement it manually, if needed.
Adding one more point to @dr. 's answer marked as accepted : Use the python package txredisapi, which uses redis protocol for twisted with connection pool support and many more.