Ok. Here goes:
"Which types provide the best coverage against all Pokemon, excluding the Tynamo line? (more than four types possible)"
The four best coverage types:
Ground, Flying, Electric, and Fighting. With those four, there are only a few types that you can't hit super-effectively:
There are a few Type COMBINATIONS that you can't hit super-effectively:
Bug/Rock ((For Example) Armaldo, Crustle)
Bug/Steel (Scizor, Durant, Forretress)
Dark/Ghost (Sableye, Spiritomb)
Water/Ground (Swampert, Seismitoad, Wooper)
Water/Dragon (Kingdra, Palkia)
Steel Will hit Fairy, as well as Bug/Rock.
Dark hits Psychic and Ghost.
Ice hits Dragon and Ground, as well as Electric/Flying.
Grass kills Swampert and company, while Fairy kills the Dark/Ghost and the Dark/Psychics. Fire hits the Steel/Bug Types.
Source: PokemonDB's type coverage checker.
In conclusion, the types you will need are:
Hope this helps.
Edit: Got rid of two other possible questions, which turned out to not be the right ones.
(Thanks to sumwun for correcting me instead of downvoting me.)
Edit #2: Added Steel, Dark, and Ice types to my conclusion.