You shouldn't have any restrictions on your Sony camera at all for taking night shots - Do you still have the DSC-H50? ; If so, you should be able to enter 'S' (shutter priority) mode, and choose a shutter speed between 1/2000 to 30 seconds. ; In 'A' (aperture priority) mode, you should be able to choose any aperture from F2.7 (at wide) to F8, and the camera will select the shutter speed between 1/2000 and 8 seconds. ; Finally, in 'M' (Manual) mode, you can actually choose any shutter speed from 1/4000 to 30 seconds AND any aperture from F2.7 to F8. ; Plus, your ISO can be fixed manually from 100-3200 or kept on auto.
I believe the only modes that restrict your shutter speeds and aperture range are the 'green camera' auto mode, the 'P' (Program) mode, and the scene modes. ; I took thousands of night shots to great effect with my H5, the forerunner to your H50...up to 30 second shutters.