I've got three sample teams ready, I want to have at least two more by the end of the month, and to show off some different mons. I'll be submitting these to RoA soon, but I'll let you guys try them out now.
Zard + PoryNido
Venu + BlastArc + Tops
Starters + Tops
I also want to talk a little bit about the cores on these teams.
Clef + Mime
As you can see, this core is on every single one of these teams. You can run Mime without Clef and Clef without Mime, but they do so well together that it's easy to just put them together. Clef has T Wave and physical attacks to help get past Mime and a few other mons that give mime trouble, mean while Mime helps with Venu, Zard the occasional Champ, and some thing that give Clef trouble. They also have some redundant coverage in t bolt, meaning that your opponent will have a hard time getting Blastoise and Kabutops to rest. Overall they're just a good combination both defensively and offensively.
Now, Mime can also work with something like Drowzee or Exeggecute to help cover opposing Mimes. This isn't as good overally, but both of those mons can do things that Clef cannot, so there are times to want to use them over Clef. Clef can also work without Mime and just be a solid mixed attacker or dual status. They don't have to be ran together, but it's hard to pass it up lots of the time.
Also note that in none of the teams have rest on Clef or Mime. There are times to run them with Rest, but your team has to want them for defensive purposes for some reason, and you have to not want to use a more solid defensive mon instead.
Pory + Nido
Pory, a passive defensive mon, and Nido, a nearly wallbreaking offensive mon, may not seem like a good combo at first. However, they cover themselves very well. NIdoking doesn't take hits very well, so getting it in is usually on a double switch or through pivoting through a wrapper/fire spinner. Things don't take Nido's attack well, but something like Blastoise from full, can be enough to scare out Nido, which is where the water wall Porygon comes in. Barring bad luck, a healthy Pory can completely wall water mons (although an unparalyzed Dewgong has a chance at beating Porygon if Pory switches into an attack), and Pory can paralyze faster mons like Mr Mime after the water mons have been taken care of. Nido can be a beast but it needs support, and Pory is great at supporting Nido.
Blast + Arc
This a solid defensive core that helps protect against fire and water spam offensive teams. In the right matchups, these two can tank entire teams. Offensively they're pretty good for each other too. Arc helps with Pory, Clef and Venu; meanwhile, Blast helps with Tops, Zard and Dragonair. Throw on some backup support with things like Pory or Tops and you have a solid core going on.
Starters
This probably shouldn't be classified as a core since they don't have the same synergy as the other ones on here, but I know this is a really cool concept and I don't want to deprive anyone of it. The concept is pretty straightforward. Blast tanks hits, Zard deals damage and Venu supports. I've talked enough about Blast in the last core. Zard can either run a Fire Spin wrap/pivoting/anti-lead set or an SD set. Venu helps take out waters that both Venu and Zard don't want to deal with and can provide sleep powder support to help out SD zard. This core has problems with Mime, so Clef is usually a good mon to go with this as well.
Electric + Flying
This is a core I work on from time to time. Electrics aren't all that great to begin with, so it's hard to justify using them over something more proven, but this isn't a bad way to use them. Putting Magneton or Electrode with Fearow, Moltres or Charizard helps wallbreak each other weaknesses. Magneton can just delete some waters and flying by clicking Thunder and Electrode can provide good support in being able to 2HKO and outspeed those mons. Meanwhile, Flyings help deal with Venu and sweep when the waters are gone.
I will share a team with the core it down here as a bonus for reading everything. It's not something I plan to add as a sample, because it's not that good and I'm not done polishing it, but if you want to use an electric, here's your chance.
Mag + Fearow
There are other cores in the meta and to be discovered later on; however this gives you a good glimpse into the cores on these particular teams.