Their daughters Beth, Penny and Holly and son Conrad (11) are already showing an interest in the maintenance and showing side of cattle breeding.
The Moiled are a hornless (polled) breed, red in colour and characteristically marked by a white line or 'finching' on the back and white under parts with red ears and red nose. But they can vary from white with red ears and nose to nearly all red. The face is often roan or flecked.
Believed to be one of the oldest native Irish breeds - they may go back to Celtic times - the Moiled population went close to extinction.
In the early 1980s they were down to 30 breeding cows held by two farmers in Northern Ireland where they are the only surviving domestic livestock native to the region.
The name Moile (or Maol) is derived from the Irish language and relates to the distinctive dome or mound on top of the head.
The Irish Moiled Cattle Society describe the breed as being "of medium size (a mature cow can weigh up to 650kg) and are generally easy to handle with a placid docile temperament with animals easily maintained on less acreage and less concentrate than most other cattle breeds".
They say that the Irish Moiled cow can be relied upon to produce a calf every 12 months, running with a bull or through AI if kept in good health and body condition.
"They will calve to a continental bull without difficulty and have sufficient milk to do a good job with the cross calf. They will continue to breed satisfactorily until at least ten years of age. Many have continued to 15 years and beyond," says the society.
Generally categorised as a dual purpose breed, on the dairy side they can give yields of up to 5,000 litres and in the suckler herd the cow will "milk off her back" to give the calf the best start in life".
Mark McConnell's second purchase was a cow which he bought from a UK breeder before establishing contact with Cork breeder, W McCarthy, from Ardkillen, Enniskeane who together with P O'Sullivan, Banemore, Ardfert, Co Kerry, combined to hold the largest Moiled population in the south.
Mark bought a number of animals from Mr McCarthy who was reducing his herd size to build up to his present level of eight cows.
"I found that they are an easy breed to keep up. The harder you keep them the healthier and the better breeders they are. The cow I had bred up to 15 years and she bred three champions. If they get over fat they are harder to get in calf," he says.
"When they are feeding a calf they milk off their back with no need for supplementary feeding and some of them would be good enough to feed two calves," he says.
Most of the animals sold out of the herd have been purchased by other breeders, but some of the breed are also being used for beef production.
There is good demand at a premium of around 25c/kg over the base beef price from restuarant owners who specialise in offering the rare breed variety on their menu.
Irish Moiled beef has become known for its superb tenderness, its highly marbled cuts and distinctive flavor.
Steers can be fattened economically on good quality forage without the need for concentrates to achieve carcase weights of 220-280kg at typically R and O grades at slaughter.
The McConnells are keen supporters of the principle of preserving rare breeds of livestock, among which the Moiled cattle are listed and are now classified as Category 4 (at risk) on the Rare Breeds Survival Trust watchlist compared with having been Category 1 (critical) in early 2000s.
"Besides the heritage the Moiled cattle have evolved to suit the Irish climate and especially the north of Ireland climate," says Carmel.
"With the world population growing rapidly it's important that such an animal that can remain fertile in such harsh conditions has its genealogy preserved to ensure such a trait continues for future generations as it will be needed to feed the world."
Moilies were popular throughout Ireland in the 1800s, but it was in the province of Ulster that they thrived. The Moilie is Ulster's original and only native cattle breed.
The Irish Moiled Society was formed in 1926 to develop the breed and create and maintain a Herd Book. Much support was attracted and cattle from all over Ireland were inspected, selected and entered in the Herd Book. For many years, as popularity of the breed grew, classes were held at the Royal Ulster Show.
However with the introduction of new, more specialised dairy and beef breeds, during the 1950s and '60s, numbers of Irish Moiled cattle began to decline.
The Society declined in parallel with the cattle numbers and was disbanded 1966.
The decline was so dramatic that by the late 1970s the breed had been reduced to less than 30 females maintained by two breeders in Northern Ireland - David Swan of Dunsilly and James Nelson of Maymore.
In 1982 the Society was revived with the encouragement of the Rare Breeds Survival Trust. Since then numbers have increased dramatically with help from both the Trust and the Genetics Department of Liverpool University. This encouragement has been greatly appreciated by the Society.
In 1998 the Society became a company limited by guarantee and also gained charitable status. A notable landmark was the Royal Mail stamp accorded to the Moiled breed in 1984.
The McConnells are one of five Moiled cattle breeders in Donegal and there are breeders listed in 18 other counties in the Republic as well as 60 breeders throughout Northern Ireland.