Statutory birth registration only started in Ireland in 1864, so prior to that you have to rely on church records, where they still exist. (Many have been lost for various reasons).
You say that William Campbell, b 1811 was RC, and that you have found a Wm baptised in 1811 in the records for St Anne?s. St Anne?s is Church of Ireland so assuming your William was RC at birth, then I doubt that you have the correct baptism.
The oldest RC church in Belfast is St Mary?s which opened in 1784 (at which time there were only a few hundred RC people living in the city). Unfortunately they have no surviving baptism records earlier than 1867. St Patrick?s RC has records from 1798 (with gaps) so they might be worth a look. At PRONI their records are on microfilms MIC 1D/66 & 67.
You could also search PRONI's in house database to see if there are any records of trials in Belfast from around 1830. Ancestry has the Belfast Newsletter on-line from 1738 onwards. You could have a look at it to see if you see the trial reported. (It was only published twice weekly then and consisted of about 4 pages, so searching through a year or so isn?t an impossible task). There are also back copies of the Newsletter in Belfast Central Library so you can view them there. In original paper format as well as in microfilm.
In the late 1700s and early 1800s the population of Belfast increased dramatically as people from an agricultural background moved there, from all over Ulster, to find work. Consequently it?s quite likely that William?s parents may not have been born in the city themselves.
William Campbell is obviously a very common name in Ireland. (There?s 652 of them in the 1901 census). Even if you do find a WC baptism in 1811 in Belfast, your problem will be in determining whether it?s the right William. Do you have his parents names from his marriage or death records?
