You are still trying to make a few bits of information fit the way you want
I was told Cox is not that common a name in the Pullans / Loughan area at the time.Who told you this? most early records will list the name of the head of household (and some records only those who had land, etc.) but there are so many people that do not show up in surviving records so there is usually no way of saying that there were only a few families named Cox in that area and then trying to fit them into a neat little family tree. In general, the longer a family has been in one particular place the more likely is that there will be various branches, perhaps not closely connected, in that area.
Question if we take the marriage of Robert Cox in 1864, father Moses Cox. Place an approx birth year of 1813 based on Tithe one gets an age of 51 years old for Robert Cox by the time he married in 1864. Is this possible at the time that someone marries after age 50?No way of saying how old a person listed in something like Tithes might be and if he is the same person as someone with the same name in another record.
My thought is there is one Moses Cox the whole time through those years, he has 4 sons in the 1831 census...4 sons in 1831? 1831 census lists number of males and females in a household but does not state relationships to head of household. Thus, 5 males could be head, 2 sons, father and an older brother, etc.
Robert seems to have married at the advanced age of 51, could Elizabeth be a 2nd wife?Does marriage certificate list his age or is this just an assumption because you are wanting him to be a certain Robert Cox? The marriage certificate will certainly list his marital status so that you will know if he was previously married. Checking the certificate is just good research and basic common sense.
Can someone give me some thought to if Robert Cox 1834 is the same man who marries in 1864 and dies in 1872 always at fishloughan?Death certificate will list his age which will answer that question. Again, it's a matter of checking certificate. You can now view these certificates on GRONI's site so there's really no excuse for not checking them yourself.
PS as mentioned before in this post Familysearch has a death of a Robert Cox in 1872 aged 79 registered in Coleraine. This appears to be the correct Robert Cox. Appears to be correct? have you viewed the actual certificate yet?
Can someone give me their thoughts on Moses Cox as to being the same man alive in Pullans in the date range c1790 - 1880?I can see no death registration for a Moses Cox anywhere in Ulster that matches this. The index is easily searcheed in a variety of sites including www,familysearch.org which is free.