I've done this with Stantler, Ursaring, Miltank (Surfer), Noctowl, Girafarig and Dunsparce.
Stantler makes for a good Screener with Intimidate. Also had a short success of using Role Play against pokemon with Water Absorb and such but his main role was just to support with Light Screen/Intimidate. Noctowl took care of using Reflect, it's very bulky in the special side so Reflect did help it survive Physical moves.
The screens really help make up with the lack of resistances for the team. Also helped Ursaring survive since I mainly used Avalanche against Lance's Dragonites. Also Guts Facade wrecks stuff. Miltank makes for a great physical wall with the screens to help heal the rest of the team as you stall. I used Scrappy to abuse Body Slam but Thick Fat could work as well if you want a more resistance-filled pokemon route.
Noctowl makes Morty so easy that I didn't even need to use Scrappy Miltank. Insomnia really helps. Also learns interesting moves like Psycho Shift, Extrasensory and Air Slash.
Along with your Normal/Flying mon, Girafarig is a must against Chuck. Early Bird Girafarig also helps against Poliwarth's Hypnosis. He is pretty frail though so Screens definitely help.
Dunsparce is pretty okay early game. STAB Headbutt flinchax is always fun. I then changed it to a Serene Grace abuser with Charge Beam, Ancient Power, Blizzard and Fire Blast. Didn't always work but it's so satisfying every time Serene Grace does its magic. It has good HP so again, screens really boost its survivability.
This was a few years ago but I do remember it was one of the more interesting monotypes since I always wanted to use a lot of Normal pokemon found in HGSS (even wanted to use mons like Kangaskhan/Dodrio from the Pokewalker). Some interesting movepools with a Normal monotype so it's not as boring as say, Water (which I got really bored of).