Not being a great fan of the Rings trilogy, although I did enjoy the films and loved The Hobbit, all I'll venture in regards to the question of their being clerics in the books in question is this: IMO there were none, as there were no deities and no places of worship, not even sacred groves for druidical ceremonies, mentioned. Religion entails rites and ceremonies overseen by a cleris--birth, death, confirmation, wedding, etc.
Well, being a great fan of the Rings trilogy, I'll venture that Col. Pladoh is correct. They are not only not mentioned, it is specifically mentioned that they don't exist.
No good being in the LotR has anything approaching a religion. That is because although all good beings in Middle Earth are aware that it has a creator - Illuvator, The One - none of these same beings knows
how Illuvator would desire to be worshiped or even
if he desires to be worshiped. Therefore, they wisely refrain from worshiping Him or anyone else. They have no religions. They have no temples. They have very very few rites. Illuvator remains for the period of all of Tolkien's stories an unrevealed god. Only the Valar know him, and so the good peoples of Middle Earth appeal to them for intercession, but they wisely refrain from actually worshiping these fellow created beings. Illuvator is explicitly active in the events of The Lord of the Rings, but he doesn't reveal himself, and indeed only the very wise (like Gandalf) are capable of recognizing his plans for what they are.
In the books themselves, we see only one instance of something approaching a religious rite. That is the moment after Frodo and Sam have become guests of Faramir just before the evening meal Faramir instructs the hobbits to turn with him and his men to face the West in silence in memory of Numenor, in honor of the Valar, and to "that which is beyond Elevnhome and will ever be". (This scene and all its surrounding context is missing completely from the movies, because beginning with the capture of the Hobbits by Faramir, PJ departs from the text significantly both in the characterization of Faramir and his subsequent actions.) Even here, it is worth noting that Faramir and company are not praying in the usual sense of the word because
they don't know how.
Elsewhere in Tolkien's works, we see only one instance of actual religious worship, and that is the custum of the Numenorian kings to offer an annual prayer on the summit of a mountain on behalf of the Numenorian people. In a strange way, the closest thing to a cleric in all the stories are the High Kings of the Numenorians - of which the best known example would be Aragorn. Of course, Aragorn doesn't fit neatly into any D&D class, as he's actually something more of a Paladin than what the D&D ranger has become. Aragorn shares with the High Kings of medieval lore and the Paladins of D&D something like a 'laying on of hands' ability, which Tolkien references strongly in the books during the Houses of Healing chapter in which Aragorn is recognized by the people of Minas Tirith as the true king because "the hands of the King are the hands of a healer".
All other acts of worship in Tolkien's works represent acts of worship of Morgoth or Sauron by false religions. In keeping with Tolkien's beliefs as a Catholic, all of these false religions tickle the fancy of Morgoth or Sauron, but they are completely vain and futile acts and Morgoth and Sauron - being less than divine beings - are unable to do any more to reward the act than any other powerful being could. So essentially, the only religions on Middle Earth at the time of The Lord of the Rings are false ones.
So, in short, no clerics, and certainly no spell casting ones. In fact, all magic occupies a rather strange place in The Lord of the Rings. Galadriel - herself a rather mystical being - tells Frodo that she doesn't know what the word means. In The Hobbit, the hobbits are said to have no magic "except that ordinary sort that allows them to disappear quietly". Yet, we can be pretty sure that hobbits don't cast spells in order to be very very quiet. In Tolkien's works, magic seems to be nothing more or less than the product extreme skill (at something), and is deemed 'magical' by the less skillful if they don't understand it. For example, much of Saruman's 'magic' in the books that we get to see could be considered to be nothing more than epic level bluff, diplomacy, craft, and knowledge skills and the cunning usage of things like gunpowder. Gandalf is definately the most wizardly being in all the books, but he's nothing like a D&D wizard and doesn't practice much anything like Vancian magic.