First off, "something not working well on mac browsers" is not a valid problem report, it's a vague indication that something may be wrong. You should be first getting information from your user as to what exactly they mean by this. Otherwise you have no idea what you're really looking for.
Then, you have few options. If you can't borrow/beg/steal a Mac for testing, you'll need to either buy one or state that it's unsupported. If you're hard up for cash, you might want to consider dropping by your local Mac store and asking to demo their latest and greatest machine, the most expensive one so they'll be more likely to give you free reign using it for 15 or 20 minutes.
That's what I'd do but I'm a sneaky cynical old guy :-)
Another alternative (if possible) would be to drop around to the client's site to check it out. This will save you both the cost of buying a Mac and endear you to the client as someone who goes out of their way to keep them happy (no good, obviously, if they're on the other side of the country).