...The same way you completed it in 2007.
It is untrue that you need to catch every Pokemon in the Sinnoh Pokedex to get the Poke Radar. If you have merely seen the first 150 Pokemon it in, you will be able to get the National Pokedex and the Poke Radar. Thanks to in-game trainers and other conveniences, version exclusivity is not an issue either.
You should be able to register all the version-exclusive Pokemon in the Sinnoh Pokedex by simply completing the adventure; but, if you're in doubt, Serebii has lists of in-game trainers who use each one. You can use these lists to find a trainer who has each of the missing Pokemon in your Pokedex, allowing you to register all of them as seen. Here are the lists for all the Pokemon in the Sinnoh Pokedex that are exclusive to Pearl: Shieldon, Bastiodon, Misdreavus, Mismagius, Glameow, Purugly.
Depending on which starter you chose, you might also be missing some of the first nine entries in the Pokedex. In that case, here are lists for Turtwig, Grotle, Torterra, Chimchar, Monferno, Infernape, Piplup, Prinplup and Empoleon.
To register Palkia, go to Celestic Town and talk to the old lady inside the house directly above the ruins. You'll be shown a picture of Palkia, which is enough to register it in your Pokedex. Here is a video showing how to do it, if you can bear the recording quality.
You will notice Manaphy is #151 in the Sinnoh Pokedex, but you don't need to register Manaphy to get the Poke Radar in Diamond and Pearl. In all Pokemon games, event Pokemon are either not required to complete the regional Pokedex or are 'seeable' through in-game means.