Parents: Charizard and Gyarados
Shared egg group: Dragon
Offspring name: Charatos
New type: Fire/Water
New base stats: 97/115/89/95/103/101
New ability and desc: Dreaded Flames - Gains a 1.5x boost to fire moves on the turn of entry, and lowers opponent's defence on entry.
Notable moves: Flare Blitz, Fire Blast, Swords Dance, Dragon Dance, Will-o-Wisp, Roost, Defog, Waterfall, Fire Blast, Overheat, Thunderpunch, Hydro Pump, Thunderbolt, Earthquake, Scald, Surf, Ice Beam
Role identification: Much like Eevee's Magmovire, this could function as many things, Mixed attacker (albeit a weaker option), DD, SD, defensive variants with WoW/Scald + Roost. Funnily enough, Gyarados gets Thunderbolt while zard gets Thunderpunch, and now they share that. Also, boltbeam. Lastly, Zard maintains it's primary role as a Dragon Dancer that doesn't care about burn. Has some good resistances to steel and fairy too.
Reserving Noivern + Mandibuzz.
Edit:
Parents: Charizard and Gyarados
Shared egg group: MEGA
Offspring name: Charatos
New type: Fire/Water
New base stats: 97/135/89/145/133/101
New ability and desc: Drought
Notable moves: Flare Blitz, Fire Blast, Swords Dance, Dragon Dance, Will-o-Wisp, Roost, Defog, Waterfall, Fire Blast, Overheat, Thunderpunch, Hydro Pump, Thunderbolt, Earthquake, Scald, Surf, Ice Beam, Solarbeam
Role identification: Amazing wallbreaker. Though it loses water stab in sun, it has nifty resistances with the typing, including 4x resists to Steel, Fire and Ice. Due to the fact that it gets near equal offenses, it can viably run a physical set as well as a special set, and it has a great 101 speed to boot.
Parents: Charizard and Gyarados
Shared egg group: MEGA
Offspring name: Charatos
New type: Fire/Dark
New base stats: 97/145/119/105/133/101
New ability and desc: Mold Breaker
Notable moves: Flare Blitz, Fire Blast, Swords Dance, Dragon Dance, Will-o-Wisp, Roost, Defog, Waterfall, Fire Blast, Overheat, Thunderpunch, Hydro Pump, Thunderbolt, Earthquake, Scald, Surf, Ice Beam
Role identification: Another excellent stat spread, Fire/Dark is usually a frail typing, but I felt that as there are too many Water/Dark mons, Fire/Dark seemed to be the way to go. Also, it's once again a Dragon Dancer that does not get burned.
Parents: Charizard and Gyarados
Shared egg group: MEGA
Offspring name: Charatos
New type: Fire/Dragon
New base stats: 97/161/122/116/103/101
New ability and desc: Tough Claws
Notable moves: Flare Blitz, Fire Blast, Swords Dance, Dragon Dance, Will-o-Wisp, Roost, Defog, Waterfall, Fire Blast, Overheat, Thunderpunch, Hydro Pump, Thunderbolt, Earthquake, Scald, Surf, Ice Beam
Role identification: An incredibly powerful variant of Charizard Mega X, better in pretty much every stat except SpA, which it doesn't need anyway. The additional boost from Dreaded Flames helps it set up as well as dish out heavy damage. There's not much getting in the way of this Eurasian dragon, and it can even run bulky sets just as well.