The upgrade evolutionary item is difficult to obtain in Pokémon Brilliant Diamond and Brilliant Pearl. You will have to go through several hoops to get it, but once you do, you will be able to use it to upgrade Porygon to Porygon-2. Here's what you need to do to find the upgrade in Pokémon Brilliant Diamond and Brilliant Pearl.
You will need to complete the entire Sinnoh PokéDex. First, you'll need to meet all the Pokémon in the Sinnoh region at least once. After doing this, you will need to return to Evisopolis, which you can find between Routes 211 and 205. When you reach this location, after encountering all the Pokémon in Sinnoh, go to the house in the far south, to the left of the City Gym. Instead, you will be able to meet Professor Oak who provides you with the Up-Grade item.
You will not be able to find this object by exploring any of the paths and you will not be able to find it before this point. This means that you will have to continue through the Pokémon game Brilliant Diamond and Brilliant Pearl, collect the Gym Badges, and then return to this area. It may take a long time to reach this point, but it is a guaranteed method of achieving it.