We already have a proper Capellan heir: Danai. That she is also Canopian is only of benefit to the Celestial Throne. No Allard-Liao mongrels need apply. ;)
Any Allard-Liao would be fairly problematic.
I don't believe any of Kai's kids are still among the living. Melissa died on Liao and David Lear passed as well. I dont recall if they had heirs.
Kuan-Yin Allard-Liao was the last Duchess of St. Ives but it seems like her pull was mostly with Sun Tzu and even then mostly on domestic social issues. Any of her heirs may be best placed for a shot at the celestial throne as they carry political clout in the CC or at least the very least St. Ives.
Cassandra Allard-Liao is apparently doing the mercenary commander thing and had at least one child with Tamas Rubinsky but demonstrates zero interest in the CC.
I recall refernce to a Quintus Allard-Liao in the Capellan Solution novels but no real details aside from that he was more involved with the FedCom than St. Ives.
Of Candace's kids, the only ones with an outside shot or even really interest in ruling the CC might, and that's a long might, be any of Kuan-Yin's heirs.
Aside from a total lack of legitimacy outside of St. Ives, none of the hypothetical Allard-Liaos can match Danai in terms of her claim. Not only do they have to overcome familial associations with individuals notorious for betraying and deserting the Confederation, unlike most of the Allard-Liaos, Danai has a history of loyalty and competent, if not always successful military and diplomatic efforts on
behalf of the Confederation. Danai probably also came closer to killing the First Prince of the Federated Suns than any Capellan in history, and in fact literally crippled him, which is a nice feather in her cap.