Hi rcuser,
Have you got his and Priscilla's marriage details?
If not there seems a very likely looking one on the free BMD
June quarter 1879 11a 798 Llanelly there is a David Rossiter - on the same list of possible spouse's for him there is a Priscilla Thomas. I would guess this maybe him if you want to order his marriage cert, if you haven't already got it yet of course
I'm thinking now maybe if he married in Llanelly then maybe he was born around that part of Carmarthenshire somewhere, or close to Llanelly anyway like Pembrey etc. (also I noticed his occupation is a tin man in the 1881 census -There was a lot of tin industry around Llanelly in those days- one of my husband's direct lines comes from Llanelly who were tinplate workers at the tinworks in Llanelly)- so perhaps going through all the ros*(wildcard) around Llanelly may find him - just a few thoughts/ideas for you. It looks like a name that could be very easily mistranscribed in most of the censuses to me .
I couldn't find his birth with a quick search of the free BMD, but it is not complete - Maybe if you search through all the free Birth index images on ancestry you may find his birth. I'm probably just suggesting things that you have probably done yourself
Anyway,back to the censuses; Like ems girl ,I couldn't find him either in the 1861 and 1871 Carmarthenshire censuses .
With a quick search ,the closest one I could find in the 61 census , born in Carmarthenshire anywhere, so happened to be living in the Llanelly area is David Rosser - but his age was a little way too out for my liking (1859) ,but that's nothing to go by of course, and it's down as Rosser, but looking at the image it could be anything. I really wouldn't like to say what this persons name is for sure, and I wouldn't like to say it's Rossiter either , it doesn't look like Rosser to me, but what it says for sure I do not know- So I won't lead you on a wild goose chase with that one I found.
If I were you, and you haven't already got it of course I would send off for his and Priscilla's marriage cert to find out what his father's name is - it may make it a little easier for you to find him in the censuses as a child .
Hope that is of some help
kind regards

P.S. I've just taken another look at the BMD, and there are a few Rossiters registered under the Llanelly district on the free BMD, there is also another David, who died in 1856 in Llanelly way before your David got married and only a few years after your David was born. Maybe it's his *father, or uncle etc, or maybe not - *I'm just totally guessing with this maybe his father of course ,without much info to go on. There is also a few possibilities for siblings for him. Hope that helps out a little bit.