Deoxys is not available to be caught in game in Pok?mon Pearl. However, he can be imported from other games by way of Pal Park. Once imported, he will appear randomly in the Mountain area of Pal Park.
The simplest method of obtaining Deoxys in Pok?mon Pearl would be to trade with another player who has him. If that option is not available, however, he can be imported from Pok?mon Emerald, FireRed or LeafGreen. All three of these games were only released for the Game Boy Advance, so players will need to have a Nintendo DS model that has the appropriate cartridge slot. Players who have a DSi or 3DS will have to trade for Deoxys.
In all three of the Game Boy Advance games, Deoxys is found on Birth Island. Getting there requires the Aurora Ticket, an item available only from Nintendo events, as a Mystery Gift or by trading with other players. Once the ticket is obtained, Birth Island can be reached by speaking to the sailor in front of the Seagallop Ferries in FireRed and LeafGreen, or by riding the S.S. Tidal in Emerald. Once on the island, the player must follow the moving rock by taking the shortest possible path to it each time it stops moving. After the rock finishes its movement pattern, Deoxys will appear.