I use an Elk M1G along with an ELK-M1RB relay board (has 8 contacts) for doing this. My garage door opener had a wall-mounted hardwired control pad. I just fished a line from it to the M1G panel and connected the wires in parallel with the existing switch. Then, I set the M1G relay contact to go open whenever it is closed using rules in the ElkRP software. Of course, you must check continuity with a volt meter while depressing the switch. If the wall switch's circuit is not simple (mine was old so it was), you may need to solder the wire onto the correct points of the PCB in order to pull the switch to ground, simulating a user press.
You'll find the M1G module for Premise is very robust. Anything that the Elk RS232 protocol allows is implemented in Premise. It will cost more initially than just a pure IP based solution, but it will pay for itself later if you want motion detectors to track occupancy, door sensors to trigger door left open reminders, etc.
Z-wave motion and door/window sensors cost too much compared to their wired counterpart. The other drawback is they require batteries and must be in wake mode (or whatever it's called) to be polled by the VRC0P. Markh added the code for this into the Premise VRC0P module though, but I don't think he added support for security sensors that use encryption. Although I haven't used any wireless solution except the old X10 sensors, I tend to think a wired solution will be much more responsive and reliable. The M1G has about a 50-100ms response time.
To give you an idea of cost: a wired door sensor is $.9-$1.10 and hard wired motion sensors are as cheap as $7. The Elk relay board I bought was very reasonable too compared to an IP based solution that had 8 contacts, but this assumes you can find a distributor willing to provide you with discounted pricing (PM if you want advice on this).
Basically, the Elk M1G is IP based after you add the Elk M1EXP serial to ethernet interface, so you still get your wish
You could also use a network based serial port server such as the Lantronix WiBox and connect to the M1G's onboard RS232 port (or to anything's RS232 port). The WiBox is very nice if you find an actual auction on ebay (not the buy it now stuff), I bought a four of them when they were cheap (far far less than the $250-$300 street price).
Whatever your approach, you want to ensure the device you use has contacts that can momentarily close, and that you can adjust the time for the closed state. 300-500 ms timing for the closed state should emulate a user press very well I think, but this may take experimenting on whatever garage door you use. You can also solder onto a spare garage door wireless opener if you want and not fish any wires.