We have in-house expertise of writing web-based datbase systems based on PHP and MySQL. Web based database systems have grown in popularity over the last few years since no work is needed to install the programme on workstations other than emailing everyone an internet address.
In most cases there is no need to pay for expensive per-user licenses, and the database system can run on an inexpensive server located on your own premises. This solution also has the advantage of running on a variety of systems. In some cases what you are looking for may have already been written and is available as an open source project.
On the other hand, you may be running other systems, and we also have in-house experience of MS Access and FileMakerPro.