I think that Solaire is not infact looking for a sun, but son. This is a fairly wild theory and based mostly off interpretation however alot of what we know of the characters can be told by the place they visit. After moving from the Undead Burg he goes to Anor Londo, it can be assumed that in his world he defeated O&S and spoke with Gwynavere, who is suspected to be a goddess of fertility, hence the generous bossom. Who better is there to bear a son. However I also feel he had a son, who most likely died. Next bit of evidence is that he next goes to Lost Izalith, home the the Bed of Chaos who represents life, (in contrast to Nito, Death), she tried to re-create the first flame, which bore the first great souls and gave the hollows "life", but failed and instead gave birth to the demon's. Her soul description even says "it's power formed a bed of life", I believe this shows he was trying to create a new son. What tipped me off to this whole idea is his dialouge when you have him from the sunlight maggots, "Was it all a lie? Have I done this all, for nothing? Oh my dear sun, what shall I do now? My sun, my dear, dear sun". He uses the possessive pronoun 'my' when talking about the sun, showing, at least, that he believes he own's it, the emotion and wording just made me think he was talking about a son, rather than sun, so I put together this theory, tell me what you think.
P.S. I don't think he is trying to resurrect a dead son, because then he would have most likely gone to the Catacombs instead, since it's filled with necromancers an' all.