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Are both of these valid?

on the periphery

in the periphery

What would be the appropriate usage? Would it be sufficient to use peripheral as a replacement?

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It depends on the context. If "the periphery" is quite a large expanse of land surrounding a city, for example, things could validly be "in" it. If it's the periphery of a circle you've just drawn in your geometry exercise book, things can only be "on" it. You can also speak of things "at the periphery". Technically speaking, a periphery is a boundary line with no thickness, but in practice we often ignore that. Exact context could also dictate whether "peripheral" is acceptable/better as a replacement. – FumbleFingers Feb 7 '12 at 5:06

Macmillan Dictionary defines periphery as:

periphery, noun : the outer part of an area, very far from the center

It includes this phrase as an example usage:

on the periphery of something: Each republic occupied a territory on the periphery of the Soviet Union.

You can also say at the periphery (the party moved so far to the right that what had been at the periphery was now the center) or along the periphery (an invisible electric fence runs along the periphery of my property).

You can say in the periphery if you are referring to the very edges of something (he drove until he caught the outline of a shed in the periphery of the truck's headlights). It's common to see economics or history textbooks (like this one) discussing countries in the core, or center, and countries in the periphery.

If something is on, in, or at the periphery, then you can say it is peripheral (peripheral republics were far from Moscow, geographically, culturally, and linguistically).

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