Battle Moveset

A Good Moveset for Sunkern would have to be this:

Attacks:

Sunny Day
Leech Seed
Toxic
SolarBeam

Items Attached:

Salac Berry

Preferred Nature:

Bold

Strategy Using Sunkern

Sunkern has some of the worst stats in the game, all of them are at a base of 30, which doesn't allow much to be done.
May aswell stick Sunny day on here, even if it doesn't faint, sunny day can always be useful, especially if you switch to a different Pokemon (or allow Sunkern to faint).
Leech seed and Toxic is basically there if you think Sunkern can survive long enough to use these moves. Solarbeam needs to be on this moveset if Sunny day is in use, and for the sake of having a higher damage inficting move.
Otherwise, there isn't much else to explain about this moveset, you know what to do, and thats not use Sunkern.

EV Corner:

Max out the EVs in Defense & Special Defense for Sunkern with any remaining in Speed

Strategy Against Sunkern

Sunkern's Defenses are both equal and really weak so any volley of attacks will kill it easily

Contest Moveset

A good Contest Moveset for Sunkern would have to be this for the Smart Contest best with Calm, Gentle, Careful, Sassy Nature:

Attacks:

Leech Seed
Grasswhistle
Giga Drain
Endeavor

Items Attached:

Green Scarf

Strategy Using Sunkern

If you do the attacks in this following order you should have very few problems; 1st - Leech seed, 2nd - Grasswhistle, 3rd - Gigadrain, 4th - Grasswhistle, 5th - Endeavor

Locations in Games

Ruby/Sapphire Trade Sunflora from Colosseum and Breed Colosseum Trade from R/S/FR/LG Fire Red/Leaf Green Trade Sunflora from Colosseum and Breed

Animé Appearences

Sunkern has had an Animé Appearence. In it, it landed frozen and got nursed back to health. After that it evolved into a Sunflora using Ash's Sun Stone Episode 189:Moving Picture!