Printed rods can be crafted by anyone with the appropriate prerequisites—most notably Craft Rod itself. For instance, an immovable rod requires Craft Rod, levitate, and 2,500 gp worth of raw materials. Someone who has those things can make an immovable rod by spending 3 eight-hour days and 200 XP, per the rules of Craft Rod itself. This is, officially, within the capabilities of such a character and does not require extra DM adjudication. Likewise with any other official printed rod. A DM is, of course, able to nix any particular rod, but that would be a houserule.
However, the rules for creating rods suggest that it may be possible to go beyond the officially printed rods—but this is firmly in the realm of DM adjudication. The rules specifically warn that
Rod costs are difficult to formularize,
and then go on to say
Refer to Table: Estimating Magic Item Gold Price Values and use the rod prices in the rod descriptions as a guideline. Creating a rod costs half the market value listed.
This winds up being rather similar to just making a wondrous item, except it’s a wondrous item that you have to hold in hand. Consider discounting the rod somewhat on that basis—it’s usually much more convenient to just wear something than it is to hold it (or, put another way, your “held items” slots are usually more valuable than other slots).