I'm not sure that would be possible unfortunately, Most routers that support the kind of software needed to easily change wifi passwords automatically need to either have custom software like OpenWRT where you can install third party packages and software, or you need to buy a router or access point that supports it.
My personal recommendation is to keep your router and invest in a good access point. You can use software like http://www.hotspotsystem.com to manage your hotspot. Now, you might be wondering about a good access point that is also inexpensive. The site claims the software supports MikroTik routerOS. MikroTik has very cheap prebuilt routers, and also routerboards. But I suggest a prebuilt, they are still cheap and at their price points some ISPs even use them and according to the people i've talked to, they work great. So definitely look into it.
