Tolkien deliberately excluded religion in Middle-earth largely to avoid having to reconcile it with his own Christian beliefs and his sense that Middle-earth was an earlier forgotten age of our world. Here are some excerpts from his letters on the point.
Letter 153
There are thus no temples or ‘churches’ or fanes in this 'world’ among 'good’ peoples. They had little or no 'religion' in the sense of worship. For help they may call on a Vala (as Elbereth), as a Catholic might on a Saint, though no doubt knowing in theory as well as he that the power of the Vala was limited and derivative. But this is a 'primitive age’: and these folk may be said to view the Valar as children view their parents or immediate adult superiors, and though they know they are subjects of the King he does not live in their country nor have there any dwelling. I do not think Hobbits practised any form of worship or prayer (unless through exceptional contact with Elves). The Númenóreans (and others of that branch of Humanity, that fought against Morgoth, even if they elected to remain in Middle-earth and did not go to Númenor: such as the Rohirrim) were pure monotheists. But there was no temple in Númenor (until Sauron introduced the cult of Morgoth).
Letter 142
The Lord of the Rings is of course a fundamentally religious and Catholic work; unconsciously so at first, but consciously in the revision. That is why I have not put in, or have cut out, practically all references to anything like 'religion’, to cults or practices, in the imaginary world. For the religious element is absorbed into the story and the symbolism.
Letter 131
Of course there was and is all the Arthurian world, but powerful as it is, it is imperfectly naturalized, associated with the soil of Britain but not with English; and does not replace what I felt to be missing. For one thing its 'faerie’ is too lavish, and fantastical, incoherent and repetitive. For another and more important thing: it is involved in, and explicitly contains the Christian religion.
For reasons which I will not elaborate, that seems to me fatal. Myth and fairy-story must, as all art, reflect and contain in solution elements of moral and religious truth (or error), but not explicit, not in the known form of the primary 'real’ world. (I am speaking, of course, of our present situation, not of ancient pagan, pre-Christian days. And I will not repeat what I tried to say in my essay, which you read.)
That said, if you want to add some form of religion to your own personal Middle-earth, you are totally free to do so. As there is essentially nothing in canon to contradict, you're free to invent it from whole cloth.