It does seem like an odd situation in many respects.
Do you have enough experience with test tools in general, and with the client's web application that you can look at the manual test cases and estimate the automation of ONE?
If not, then you could:
- grab a trial version of one tool (preferably one that has a probability of being chosen)
- get the documentation for one of the manual tests
- automate it
- use what you have learned to prepare an estimate
- make sure to include plenty of extra time to allow for an unfamiliar tool