Pokémon Diamond and Pearl/Pal Park

To unlock Pal Park you must acquire the national dex(to get that you must finish the Shinou dex). To use Pal Park you insert a GBA game into the DS GBA slot.

Ruby Version

 * Seedot -- Hakutai Forest, Route 203, Route 204
 * Nuzleaf -- Route 229
 * Mawile -- Iron Island
 * Zangoose -- Route 208
 * Solrock -- Thrust Lake, Thrust Lake Surroundings, Wisdom Lake, Aspiration Lake, Tengan Mountain, Departure Springs, Return Cave

Sapphire Version

 * Lotad -- Route 203, 204, 205 North, 212 South
 * Lombre -- Route 212 South, 229
 * Sableye -- Iron Island
 * Seviper -- Route 208
 * Lunatone -- Thrust Lake, Thrust Lake Surroundings, Wisdom Lake, Aspiration Lake, Tengan Mountain, Departure Springs, Return Cave

Emerald Version

 * Pineco -- Hakutai Forest, Route 203, 204, 229
 * Gligar -- Hard Mountain, Route 206, 207, 214, 215, 227
 * Shuckle -- Route 224
 * Teddiursa -- Route 211, Wisdom Lake
 * Ursaring -- Wisdom Lake, Route 216, 217

FireRed Version

 * Caterpie -- Route 204 South
 * Metapod -- Hakutai Forest
 * Ekans -- Route 212 South
 * Arbok -- Safari Zone
 * Growlithe -- Route 201, 202
 * Elekid -- Route 204 South, Powerplant

LeafGreen Version

 * Weedle -- Route 204 South
 * Kakuna -- Hakutai Forest
 * Sandshrew -- Lost Cave
 * Sandslash -- Route 228
 * Vulpix -- Route 209
 * Magby -- Hard Mountain, Route 227

Any Pokemon GBA Cartridge

 * Haunter -- Forest Mansion
 * Gengar -- Forest Mansion Room with eyes

also if you do it right your other game should get a mew