I agree whole-heartedly with Arpit Mohan: the era of having proprietary languages is behind us. I've seen the following scenario play out a half-dozen times in my career:
In the 21st Century, the likelihood that zero existing scripting languages will meet the demands of your product is pretty small, so... the most responsible approach, in my opinion, is to try (partially) integrating at least three existing scripting languages before giving up. This page provides a list of likely candidates. If you're not sure where to start, just pick these three:
Choose a common, high-value scenario and add scripting support for it using these three scripting languages. Evaluate the results, then pick the one the team likes best and add more thorough bindings to your API. At the end of the day, you will probably find that it works fine for your needs. If not, the exercise will, at a minimum, expose the pain points of existing languages, and provide data to justify development of a home-grown scripting language.
I'm pretty biased on this after getting burned a few times by well-meaning colleagues who got permission to design their own 'pet' language and then disappeared, saddling the rest of the team with the burden of supporting their 'Franken-script'. I'm sure there are cases where a home-brewed scripting language is justified, but... I've not personally run into them in my neck of the software development woods...