Hi potseal, what do you mean with auto-reset?
You have your control voltage going to "high", after one second the relay should activate, and when the control voltage goes back to low the relay instantly should go off?
That's the basic "on-delay" type.
You can get this from your omron device by connecting term. 3+6 and using mode A.
If you only want a short impules from the relay, you Need mode F.
See the Manual herehttp://www.farnell.com/datasheets/1500432.pdf
I don't know what distributors and relay manufacturers you use. In europe, I would go to farnell or RS Website and look for omron, tele, ABB, panasonic, eaton, finder... din-rail mount relays. They start at 40 bucks. Watch for UL or other markings you need for the US.
One second is long to wait for an automatic door, I would recommend an adjustable relay. Maybe it will work fine with 0.2-0.5 sec only.