Any reduction gear box having a reduction ratio of 1:2 can be used in reverse to obtained the doubling of the speed of rotation. Just make sure that the gear material is of quality. The torque values that the gears will be experiencing will be very high which can easily break them.
This number 2 of increasing the input speed is not good for reasons of gearbox durability. You have to change it to 2+ or 2- by a pertinent changing by 1 of the number of teeth of the larger gear.
There is a number of things to take into account when selecting/designing a suitable gearbox. Of course, the arrangement of rotational axes drastically influences the topology; if they are parallel, you can use regular spur gears; if they are concentric, you might need a planetary gearset (or two sprockets); if they are angled, you obviously need something more exotic. As Theodore Costopoulos said, you don't want one gear to have exactly twice the teeth of the other. This will cause uneven wear, as one tooth on the first gear will always hit the exact same tooth on the second.
It's difficult to advise you on your problem without more detailed information about the loadcases and mechanical arrangement (shafts & bearings). I'd be happy to help you if you could provide some drawings.
To double output speed the simple method would be to have an appropriately sized input gear (Appropriate for load & space constraints), the output gear needs to have twice the number of teeth (assuming a spur gear is used). For an in- line requirement the concept is the same, but a planetary configuration would be more suited.