Advice for P-Channel Mosfet in Depletion Mode
Depletion mode devices are quite rare and expensive. In general, it is best if you find other methods such as using a normally-closed pushbutton instead of a normally-open pushbutton, or devise an inversion or latching circuit that uses more common enhancement mode parts.



UPDATE:

You said you want the LED to be off for as long as the button is held (i.e. not a latch).

Just use a normally-closed pushbutton. If you can't find one, it's easy enough to just use a normally open pushbutton in parallel to steer the current away from the LED to turn it off.

You can divert current through a regular diode (D1) that has a lower Vf than the LED. This will produce a voltage across the LED that is not enough to turn it on.

You don't actually need D1 and can use a true short-circuit across the LED to keep it off. But your R2 has to be high enough resistance or high enough wattage to tolerate the heat. D1 just helps reduce current when the button is pressed.







simulate this circuit &ndash; Schematic created using CircuitLab

But if you must use a transistor, you can always do this. It's pointless, but you can do it.







simulate this circuit