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There is one that works really, really well, however since the avalon was never equipped with a backup camera from the factory the only way to go is aftermarket and can be pretty expensive.
This is the part you need, click here.
You will need that adapter to interface with the navigation ECU in the trunk to display it on the factory screen up front, and you will also need to pick out any camera of your choice. Many can be had for $50 or so off ebay.
It is actually really easy to install it, there are 3 wires you need to hook up. A power wire switched with ACC key on, the reverse wire from the reverse lamps, and ground. There is one "T" plug that you will unplug one of the connectors on the back of the navigation ECU (it is in the rear, drivers side corner of the trunk under the carpet on the wall). You plug one end from the NAV-TV box's harness into the navigation ECU, and then plug in the connector you unplugged from the nav ECU into the other end of the T harness. All in all, you can have it done in about an hour. I've installed a bunch of these, and never had any issues with any of them, they work great. As I said the module box itself is kind of expensive, but is the only way you are going to interact a backup camera into the factory nav screen in the dash.