I'm happy to stand corrected, but as of May 2014, it seems to me the current state of affairs in regards to database libraries, is:
1) there are no database libraries that provide access to the well-known NoSQL databases, such as Mongo or ArangoDB. There are a couple of libraries that implement their own lightweight NoSQL database, such as the one created by Andre Garzia.
2) all the SQL libraries seem to focus on CRUD operations (creating, reading and manipulating data in existing database tables), but none of them seems to support DATABASE operations - ie., such as creating a database, defining and manipulating tables. They seem to expect you to already have your database with all its tables correctly setup, and want only to put and retrieve data in them from your LiveCode app.
3) The SQL libraries I've checked are concerned mostly with providing "sql-neutral" ways of accessing the data in various SQL implementations - ie., you are able to write the same query or update statement, whether your data is in an SQLite or a MySQL database. This is because LiveCode's native database library does not do that - it merely pipes your sql to the database you specify, then converts the response from sql to a usable livecode object on return. If you are only dealing with one database engine, and are already familiar with the SQL used by it, you probably do not need a third-party library.
4) Part of the Kickstarter campaign goals was the development of a NEW database library. Although this is still quite a long way away from materialising - there are many other goals the LiveCode team has to deliver before this particular one - depending on your budget and time constrains, it may be better to work with the existing built-in functions, and wait and see what will be on offer "out-of-the-box" a year or so from now.
In terms of SQL database support, what I would really like to see, would be for someone to develop something akin to RedBeanPHP, for LiveCode:
http://redbeanphp.com
This php library allows the programmer to code without even knowing how the data is being structured in the underlying database. The library creates the database scheme on-the-fly, as the code requires it... From the programmer's perspective, this adds several of the benefits of a NoSQL database to an SQL engine.
I hope this information helps.