First thing you should know is that Red's team is all in the mid-high seventies with the exception of Pikachu, who is Lv. 81, so your team is probably going to need to be levelled up more if you're to stand any chance of winning. Here's some attempts at movesets for you:
Typhlosion @ Charcoal (for lack of anything better, really)
- Flamethrower
- ThunderPunch
- DynamicPunch
- Filler Move
Basically just to give you extra coverage, since you can get TM's for the elemental punches in G/S/C if I remember right. The fourth move can be pretty much anything you like.
Snorlax @ Mint Berry
- Return
- Shadow Ball
- Earthquake
- Rest
Stick to physical attacks for Snorlax - his Attack outstrips his Sp.Attack by a fair margin. Shadow Ball and Earthquake are the best you'll get here, but if you don't have those moves available, just stick to whatever physical/stalling moves you have. None of Red's Pokemon resist Normal-type moves, so you've got a fair amount of leeway with what moves you pick here.
Dragonite @ Bitter Berry
- Outrage
- ExtremeSpeed
- Ice Beam
- Thunderbolt
Draggy's Gen II physical movepool is poor compared to his Special movepool, so he can go Special Sweeper here. Flamethrower, Thunderbolt and Ice Beam are all from the Crystal move tutor, and I've left ExtremeSpeed in there to make up for Draggy's low Speed stat.
Suicune @ Leftovers
- Surf
- Ice Beam
- Mirror Coat
- Rest
Stally Suicune, basically. Mirror Coat will waste Venusaur and Pikachu if you survive their attack (pretty big "if" there, so be careful) and will finish Espeon too if it tries to Psychic you. Surf and Ice Beam to cause some damage, and Rest to keep you alive, basically.
I've got nothing on Gyarados unfortunately - his Gen II movepool seems pretty horrible, and I've not been able to come up with anything from it unfortunately. Also, make sure to have Igglybuff in your team for added support - its presence in the battle is absolutely crucial for victory, as much as sarcasm is necessary for humour and wit.