I have made several nose cones out of water bottles. If you get one that is a usable diameter, you still have to worry about what to do about that pesky cap. I have foamed the cone and then formed a tip from that...and I have even just left it on.
From the water rocket world comes a better technique. In the video, the rocketeer forms the tip by a combination of grinding and melting. I don't have a bench grinder and don't know if a hand drill or my cheap press will be fast enough. I may experiment with what I do have just for kicks and to kill time while paint dries.