We've developed a simple timesheet software for our own internal use. With small changes, it might be appropriate for you to use.
On your low budget, we may offer you with the following features:
- login and registration allows different user accounts
- users may track time by a simple button-click. time entrys may be tagged and described for further analysis.
- a weekly PDF export can be sent to the user's email address
The software is completely based on HTML5/JavaScript and can be delivered as a Website or as a Desktop app (Windows, Linux, Mac OS).
Do you have a more detailed project description? It would be nice to hear, if you need additional features.