The question Caleb linked shows several options for Controller support.
- Use a program to map the Controller to Keyboard and Mouse presses, like XPadder.
- The Minecraft Joypad/Splitscreen Mod can also be used, and is far more integrated into the game (Tooltips and such). The XBox Gamepad is natively supported. Supports 1.6.4, 1.7.2 and 1.7.10 using Forge.
Looking around for a bit on reddit, your best bet seems to be CJB's QuickCraft. I think you will still have to deal with moving a cursor with a gamepad, but at least there's no dragging items into the grid.
According to the website, the latest version is for MC 1.6.4, though another site lists it for 1.7.2/4 as well, so you might try it out (If you do, feel free to comment or edit the results into this answer).