Eggs in a convection microwave
Assuming that you are going to use your convection microwave without the microwave function, your question boils down to "How do I boil or bake an egg in a (toaster) oven?".

The answer? Slowly.
In an oven, heat transfer is via air, which is a way worse conductor than water. So you put your eggs either directly on the grill rack or in a small container. Many sources recommend a metal muffin tray, because all the hot eggs han be handeled at once and in the rare case of breakage, the mess is contained. Temperature recommendations vary a bit, but for hard boiled eggs, the rule of thumb is:


  30 minutes at 160-180 C / 320-355 F


A word of warning:
Do not bake your eggs too long!
If the temperature of the egg exceeds the boiling temperature, the water in the egg turns into steam and you have created a little egg-bomb, which may go off inside your oven or while you are handling the hot egg. The effect is better known from failed attempts at boiling eggs in a microwave, but the danger is real.