Hi King... So sorry for not getting back... but I gave up on looking for any Rice information, as all I was hitting was brickwalls.
Butttt... Within the last month new information has been opened in Ancestry and I can now tell you that William (1844) & Robert (1846) came from Ballynagarrick, Co Down. Another researcher had information from Knockamuckley Church that these boys were living (separately) with uncles in Ballynagarrick. William (15) lived with uncle William (42) & family. Robert (11) lived with John (50 - farmer) and family. John's 2 sons immigrated to NZ in the 1860's and 2 possible sons ended up in VIC, Aust.
John (s/o John) married Sarah Patton in Armagh and is listed as Ch o E. Will (1844- Aust; 1842-Ballyna) & Robert (1846) are listed as Ch o E.
There was an entry for a James Rice marrying and Eliza/beth Toppin (Topham more likely, they lived Ballydougan) in Nov 1841, which fits for William's Irish dates.
Interestingly... the entries in the Church survey of 1857 lists the father of William & Robert as 'father in America'. Once upon a time, I did find a message looking for a James Rice who had to leave Co Down under suspicious circumsatnces. they listed John rice SR and James's father and John Rice JR as brother (these would be the Rice's of Ballynagarrick from the Valuation). I recall that they said their family legend was that James arrived in the USA, under a different name because he may have been wanted for doing something to his Landlord.
Also, a HANS rice lived near John Rice (s/o John) and had one of John's sons-in-law look after his will.
Once again sorry for not getting back sooner... and if anyone can find/recall information on a James rice who maybe fled Co. Down to USA... before 1857... Would love to hear from you...
Cheers..