The first two zones of PokéPark Wii have 31 and 26 Pokémon. Here is how to befriend each one, based on the Poképédia list. The number is the one from the friend guide.

Meadow Zone

No.PokémonHow to become friends
P-001ChatotBeat it in a race
P-002ChikoritaAfter seeing it in the Meadow Zone
P-003TurtwigBeat it in a race after talking to Treecko on the first bridge
P-004TorterraBeat it in a battle after winning Venusaur’s attraction
P-005BunearyBeat it in a race
P-006MunchlaxBy giving it a Big Berry after winning Bulbasaur’s first crystal
P-007TreeckoBeat it in a race
P-008MankeyBeat it in a battle on the second bridge
P-009BidoofAfter helping it build its house
P-010BibarelBeat it in a battle when it arrives in the zone after you finish helping Bidoof
P-011OddishBeat it at hide-and-seek
P-012AipomBeat it in a race
P-013AmbipomBeat it in a battle after befriending Aipom.
P-014LeafeonHave 20 friends, then beat it in a race
P-015SpearowComplete the course
P-016CroagunkBeat it in a battle after visiting Venusaur
P-017StarlyBeat it in a race after getting Venusaur’s crystal and talking to it on the road to the Central Square
P-018BonslyBeat it at hide-and-seek after befriending Turtwig
P-019SudowoodoBeat it at hide-and-seek after befriending Bonsly
P-020PachirisuBeat it in a race after befriending Turtwig
P-021LotadBeat it in a battle after befriending Buneary
P-022ShinxBeat it in a race after befriending Buneary
P-023ScytherBeat it in a battle after befriending Croagunk
P-024MagikarpBeat it in a race after getting it out of the water (by hitting it with Thunderbolt)
P-025CaterpieBeat it in a race after using Dash on the tree between the two bridges
P-026ButterfreeBeat it in a race after befriending Caterpie
P-027WeedleBeat it in a battle after using Dash on the tree on the path to Magikarp
P-028ShroomishBeat it in a race after destroying the crate “behind” Magikarp
P-029TropiusGive it a Big Berry after befriending Munchlax
P-030BulbasaurWin Bulbasaur’s Daring Dash
P-031VenusaurTalk to it after reconciling it with Empoleon and Blaziken

Beach Zone

No.PokémonHow to become friends
P-032PiplupAfter seeing it in the Beach Zone
P-033SlowpokeBeat it in a race
P-034AzurillBeat it in a race
P-035CorsolaAnswer its quiz correctly
P-036WynautAfter building the first bridge
P-037CarvanhaAfter completing Pelipper’s Circle Circuit
P-038SharpedoAfter completing Pelipper’s Circle Circuit
P-039WailordBy recycling bottles
P-040TotodileBeat it in a battle after befriending Azurill
P-041FeraligatrBeat it in a battle after completing Gyarados’ Aqua Dash
P-042LaprasAfter crossing the sea and asking it to return to the Beach Zone
P-043PsyduckBeat it at hide-and-seek
P-044GolduckBeat it in a battle after befriending Psyduck
P-045BuizelBeat it in a race
P-046FloatzelBeat it in a race after befriending Buizel
P-047VaporeonBeat it in a race after making 30 friends
P-048MudkipBeat it at hide-and-seek after befriending Slowpoke
P-049TaillowBeat it in a race
P-050StaraviaBeat it in a battle
P-051PidgeottoBeat it in a battle
P-052KrabbyBeat it in a race after recycling bottles
P-053CorphishBeat it in a battle after recycling bottles
P-054BlastoiseBeat it in a battle in the Granite Zone
P-055WingullBeat it in a race
P-056PelipperWin Pelipper’s Circle Circuit
P-057GyaradosWin Gyarados’ Aqua Dash