After spending literally hours trying to fix the issues with the wireless 360 controller, I found a solution. With this, you are able to shoot from cover and vibration/rumble is working.
I also tried this with Assassin's Creed 2 and it works like charm. Finally have rumble which was missing in Khemitude's fix. I am assuming that this will also work in all Ubisoft titles that is compatible with Xinput/360 controlllers.
(Tested using MS Xbox 360 Accessories 1.2 on Windows 7 32-bit.)
1. Download XBOX 360 Controller Emulator here and extract it somewhere.
2. Turn your wireless controller on and run x360ce.exe. It will ask if you want to create the default x360ce.ini and xinput1_3.dll, click yes to both.
3. In the general tab for controller 1, under presets, select "Controller (Xbox 360 Wireless Receiver for Windows)" and then click load.
4. In the options tab, under Fake API, select "EnabledUsb" for Fake WMI and "EnabledCallback" for Fake DI. Also uncheck "Use Init Beep" under Testing and Logging. Don't change any other settings. Click save on the bottom right and close the program.
5. In the folder where you extracted x360ce.exe, you should find the generated x360ce.ini and xinput1_3.dll. Copy both files to the main program directory where the game executable is. For Conviction, it can be found at X:\Program Files\Ubisoft\Tom Clancy's Splinter Cell Conviction\src\system.
6. Run the game and enjoy your independent analog triggers and working rumble.
All credit goes to the x360ce developers (google code project page can be found here) for providing a way to fix the travesty that is the wireless 360 controller. In fairness to Ubisoft, this isn't just their problem but Microsoft's as well. For some stupid reason, they decided that it was a good idea to put the right and left trigger on the same axis thus causing them to not register when simultaneously pressed. Fail.