Daikari
I'm actually not sure what's going through the mind of Daikari supporters. Yes, Daisuke had a very clear attraction to Hikari, and extreme jealousy of Takeru, but Hikari always rebuffed his passes. Perhaps they feel that Daisuke's persistance would eventually overcome any reluctance on Hikari's part, or perhaps they just felt that he ought to get to win out for once. In either case, there is not good evidence for a mutual relationship, or for compatible personalities.
Daikari is one of the more obvious shippings, due to Daisuke's constant quest to woo Hikari and put down Takeru -- or is it Taberu? Entire subplots are devoted to Daisuke pining over his indifferent goddess. But, in truth, Hikari is more than indifferent to Daisuke's attempts to win her over -- and we're most of us cheering when, after being put down because he was dissing his sister, Daisuke mourned, "she loves me, she hates me, she loves me, she haaates meeee!" complete with image of him falling down a dark hole. And weren't we also encouraging him to fall into such deep despair at that that he would throw himself off the conveniently-placed cliff next to him? After all, he didn't really have much to recommend him back then.
Daisuke's philosophy as to why he should have Hikari is also doubtful. Was it because he was leader, and therefore entitled to any girl he desired? Was it because he was "there first" -- despite the fact that that's untrue? Or was it that he was such a star basketball and soccer player that she should, of course, instantly fall in love with him? In any case, it was either a matter of not thinking, of not understanding, or of insulting Hikari's intelligence and sensitivities.
If you are going to go with a show-supported coupling, Takari is the answer. If you are looking for something different, Koushari, Daiyako, and Taisuke are better options. Of course, that's just my opinion. Why don't you tell me if you think otherwise?