Out of the box:
There is, sort of, It's called delay on make and delay on break with a monostable output. The devices may likely be found in a "multi-function timer".
What you could do is use a "smart relay". These would satisfy your "off the shelf" minus the programming. Idec, schneider electric and there's Teco - **broken link removed**
Cost, unfortunately, tends to do weird things.
I know your asking for Start/Stop right now, but there could be other functions that are needed.
e.g. Oil level low prevents start and causes alarm
Input must be valid for some time before it's taken as valid.
Exercise of generator - usually done in xfer switch.
You really don't want the states to get messed up. So, other inputs can actually verify what's expected. e.g. engine running and engine stopped.
Some scenarios. What if the generator is exercising and you get a power fail wanting the generator to start? The generator is already running.
Think carefully.