I don't have any specific experience in the field but I'd imagine that there is probably not a huge amount of software that is targeted at such a small niche - most commercial software is likely very large systems integrated into large commercial airlines where they have 1000s of routes to cater for, and is thus likely very expensive compared to the needs/budget of a small service like you've described.

If simple searching for something applicable doesn't turn up a suitable option, consider this:

Build the system, and keep in mind (without letting it massively delay delivery of a working product) that if it's built well, it can probably be licensed to other small operators as well. Not necessarily as a means of making profit, but simply as a way to recoup costs.

Good luck!