I have a D&D 3.5e cleric with the Time and Travel bonus domains and no specific patron deity (bonus domains based on personal beliefs and inclinations). This cleric meets all of the requirements for becoming a Radiant Servant of Pelor except Pelor is not his patron deity yet (though his personal beliefs could align with those of clerics of Pelor rather nicely). If my cleric adopts Pelor as a patron deity now, what would that mean? And what would that mean for his current bonus domains?
Pelor's domains are, as per Complete Divine p. 117, Glory, Good, Healing, Strength and Sun. Neither Time nor Travel are amongst them, so you need to convert. As per this question you'll be needing a Divine Conversion:
A cleric who changes his patron deity must complete a quest to prove his devotion to his new patron. The nature of the quest depends on the deity, and it always clearly reflects the deity’s alignment as well as his or her goals and beliefs. To start the process, the cleric must voluntarily accept a geas/quest spell cast by a higher-level cleric of his new deity. During the quest, the cleric has no access to spells or cleric class features—except his weapon and armor proficiencies, which he does not forfeit.
Upon completing the quest, the cleric receives the benefit of an atonement spell from a cleric of the new deity. The character then becomes a cleric of the new deity and is inducted into the clergy during an appropriate ceremony of the DM’s choosing. After selecting two of the new deity’s domains in lieu of his old ones, the character has all the powers and abilities of his previous cleric level, plus the granted powers of his new domains.
By doing this you'll be meeting the last two requirements of the Radiant Servant of Pelor prestige class: you're a servant of Pelor and through that get the Sun domain. Of course, this'll mean you'll lose the Time and Travel domains, but it's a small sacrifice to make in the name of Pelor.
Alternate take: Pelor, the traveling sun.
Another option would be to worship Pelor in his aspect of the moving sun. The sun after all travels from one horizon to the other during the day and it is used to measure time. As such, Pelor covers these two domains even if they're not in the books. Replacing the Sun domain with Time and Travel does not severely alter how the Prestige Class works (though the Radiance feature becomes less useful). Propose this to your DM and see where it takes you.