To answer your technical question: You don't want to write your own language and interpreter. That's too much work for you to do. So pick some other language, say Python or Lua, and look for the documentation that lets your C program hand it blocks of code to execute. Of course, the script needs to be able to do something, so you'll need to find how to expose your program's objects to the script. Also, what will happen if a client is running the program when you update its source code in the database? Should the client restart? Are you going to store the entire program as a single row in this database, or did you want to store individual functions? That affects how you structure your updates.
To address other issues with your question: Why do you want to do this? Making "interpreted language" part of your design spec for a system is not often a good sign. Is the real requirement something like this: "I update the program often and I want users to always have the latest copy?" If so, there are other, better ways to go about this (just give us your actual scenario and requirements).