He joins the Marines. He ends up partnered with Helmeppo (the yellow haired asshole son of Captain Morgan) and they start very small. One day, Vice Admiral Garp arrives to oversee Morgan's transfer. He escapes but not before Coby and Helmeppo try to stop him (they fail). Impressed by their bravery, Garp takes them under his wing.
After Enies Lobby, Garp arrives to Water Seven and we learn he's Luffy's grandfather. He brought along Coby and Helmeppo, both much stronger and taller (though still no match for Luffy and Zoro). We later see the two of them during Marineford, where Coby manages to delay the war so Shanks can come in and stop it for good. We also learn Coby has Haki.
Following the time-skip, he's worked his way up to Captain.