Unless stated otherwise, nothing in this post is drawn from ancient sources. Most of it isn't even UPG. It's a thought exercise. Way back when I was still doing the Pagan Blog Project posts, I wrote about genealogy of the Gods. I ended that post with the following:

"One sad part of studying Divine genealogy is that there is an end. The lives of the Gods have come to a halt. We rehash the stories but no more children are born, no heroes rise. It makes me wish for the inclusion and revelation of UPG into Hellenismos. New blood, new stories, could really benefit the practice and believes of Hellenic practitioners. A new Divine child to shake up the pantheon, a new child of Zeus who grows up to fight new (or returned) monsters. Sacrilege, some say, and they might be right. But I admit to staring at the pages of genealogy in my book and wishing the lines, somehow, someway, extend to include more of the Divine family. "

I still feel that way. I still wish for a line that continues onto now. But, seeing as we don't have that, I'm going to make another mental leap. I'm going to see who of the Theoi would oversee some of the modern marvels, should They be willing to adopt them.

The internet and the telephone
It's one of humanities greatest achievements; a real-time communication link between every person on the planet who has access to a computer and a subscription. It's not one thing; it's housed on computers everywhere, everyone adding a small part to it, so you can read these words from any place in the world. I'm quite sure who would have this marvel in their portfolio: Iris, rainbow Goddess of communication, who delivers Her messages as fast and the wind and who has always been a connector; in ancient Hellas, She connected the Theoi and mankind. Her speed, Her messenger spirit, and her ability to connect everyone anywhere in the world make Her an excellent candidate for the position of Patroness of the Internet.
For most of the same reasons, I would also place the telephone firmly under Her domain.

Planes, trains and automobiles
I'm staying with the sky Gods on this one; airplanes, trains and cars have cut down travel time, have made goods readily available anywhere in the world, have allowed us to expand modern life to parts of the world where this was absolutely impossible before, and--in the case of airplanes--have given us entrance into Zeus' domain. yet, I don't feel Zeus would oversee flight. I think that would be Hermes' task. Airplanes would be a marvelous novelty for Hermes, who is known to fly everywhere. It's this huge, bulky, thing that miraculously stays in the air. I think Hermes would get a kick out of throwing a few air pockets in the way of a plane--just to see the panic on everyone's faces--before helping the plane land safely. Trains and cars go fast, make a lot of noise and are constantly out on the road. This, too, would make Hermes happy. Hēphaistos may be involved with the construction of these travel aids, but Hermes would watch over your safety while in them.

As already discussed a bit with the internet, modern life would change dramatically if we lost computers. they help us communicate, solve problems beyond our natural capabilities, provide entertainment, allow us to make a living and that's just scratching the surface of its usefulness. For me, this is another no-brainer: Hēphaistos. If Daidalos had been a Theos, I would have picked him. Athena's analytical mind may have had a part in its creation as well, but the actual tinkering bits would speak to Hēphaistos far more than to Athena. Once the first computer was completed, I would see it likely Athena lost interest, while Hēphaistos would relish the challenge of improving upon it again and again.

The radio and television
A slightly older means of communication, but none the less very valuable. Radio signals connect people, are used in jobs like airport control, security and construction, and bring music to the masses. Because of the broad application of the radio, and especially because of the music, I'm picking Apollon for this one. Anything that brings music all over the world would interest him greatly. Because of its ability to amuse, educate and spread awareness, the television would also fall under Apollon's domain.

Bombs, guns, tanks and other weapons of war
It's a cheap shot, but for their sheer destructive power, I would place any weapon of war under Ares' domain. It may not be honorable, but weapons of war are effective. When His rage reaches the point of no return, I'm sure His hands would itch to just wipe out the enemy. In fact, I think Ares would have felt a whole lot better if He would have been able to decimate the Hellenic army besieging Troy with a few powerful bombs. He is still the Lord of War. As for some of the other war-like Theoi; I think Athena and Zeus would find these methods too crude and/or imprecise. They would like the sniper rifle and, perhaps, to tinker with the missile guidance systems, but actual weapons of mass destruction? Not so much.

This is a top-of-my-head list. Are there others you have ideas about? I'm sure Aphrodite would be happy with the invention of sex toys, and Apollon with electric lights, for example. I'd also really love to hear if you had envisioned other Theoi with these examples. Have fun!