I have not tested and those are a lot of restrictions, but here is my crack at it.
Pokémon - 10
4 Volcanion-EX PR-XY XY173
3 Volcanion STS 25
2 Flareon-EX GEN 128
1 Beedrill-EX PR-XY XY157
Trainer Cards - 38
4 Professor Sycamore BKP 107
3 N FAC 105
2 Lysandre AOR 78
2 Pokémon Fan Club FLF 94
1 Delinquent BKP 98
1 Hex Maniac AOR 75
1 Professor Kukui SM 128
4 Acro Bike PRC 122
4 Ultra Ball FAC 113
3 Energy Retrieval SM 116
2 VS Seeker PHF 109
2 Switch SM 132
1 Trainers' Mail ROS 92
1 Dive Ball PRC 125
1 Escape Rope PRC 127
1 Super Rod BKT 149
2 Float Stone BKT 137
2 Scorched Earth FAC 110
1 Faded Town AOR 73
Energy - 12
12 Fire Energy
Like I said up top. I haven't tested this and I tried to keep some budgetary constraints in mind with some of my card choices (Example, I left off Fighting Fury Belt which could pretty easily be added if you want). The overall gist of this deck looks a whole lot closer to some of the older Volcanion decks I remember seeing prior to some of the more innovative minds running things like Sky Field + Hoopa EX + Parallel City. Speaking of Parallel City. There isn't much reason for you to run it in this particular deck. I honestly think the Delinquent will have more disruption. Finally, If the Sycamores are too heavy due to only having 2 VS Seekers, you could swap out for another N and another Kukui. The main point though is that I think you need as much draw support as possible with this one.
Oh, and why Beedrill EX? Because it is literally the only way to not be absolutely murdered by Garbodor while not taking a turn to Lysandre it up. Yeah, you took a turn with Beedrill, but hopefully you got more than one tool on that attack
That one is controversial though, so if you don't like it, feel free to cut it
One other thing I had considered was 4x Puzzle of Time, but honestly I think that might be a hard sell for this deck even with the extra room afforded by not having the Trainer's Mail + 4x VS Seeker.
Hope it helps. Also, anyone else who wants to add suggestions, feel free. This was put together on the fly, so I might have missed some options