Rubber woofer cone?

Very easy to do yourself.

Agree with Nsgarch, but I wouldn't bother to remove the woofer from the enclosure. I'd just lay the whole speaker down on it's back.

I'd contact Opera and double check on what type of glue to use. I don't know your speakers, but if the dustcap was designed to also add rigidity to the woofer when it's in motion, they may specify a "harder" glue than contact cement.

It should be repaired. The two main reasons are:

1.) To protect the voice coil from dust, and particles getting into the magnetic gap, and
2.) To maintain the mass and surface area of the woofer cone.

If you want to do it yourself, take the woofer out of the enclosure and set it on a flat surface facing up. Take the dustcover (that's what it's called) and get some contact cement (the kind with the brush in the bottle, not the tube) and dab a bead of cement right on the edge of the dustcover all the way around. Then set it back in place making sure it's centered (you can use the old ring of dried cement as a guide) and let it sit for at least an hour. That should do it. Tip: to make the dustcover easy to handle once you have the cement on it, first tape a loop of masking tape across the front of it that you can use as a handle. Remove it after the cement has dried.

Otherwise, if you live in or near a large city, you could have a speaker repair service do it for you.