Oh what a good idea, and how does the OP do that, snap her fingers and instantly it's done - do tell how?
Do you actually know how? I do find people like to blurt that out, as if no one ever thought of it before and as if it can be done instantly... with no actual clue as to how it would be done or what would be involved.
It would involve first, preventing the dog from seeing the cat most of the time.
This could be done by covering the fence (I would, as this is likely to be a long term issue) and if it is the OP's fence, put an inward overhang on it so the dog cannot jump over or get anywhere near reaching the top, but of a construction that doesn't allow the cat to walk on it, stock fencing would do.
You can also achieve this by only doing supervised garden trips, dog dragging a long line from a harness (never from a collar, that's dangerous).
Next, reward the ever loving crap out of the dog every time they see the cat, don't wait for the dog to bark or if the dog is barking, don't ask them to shut up or wait for them to stop. Just drop bits of sausage in front of them/shove it in their mouth (ideally get in there before barking occurs).
The point is to create a positive association between sight of cat and nice things from owner, whilst preventing barking from becoming a habit (barking is fun, its also rewarded if the cat goes away, double whammy of reinforcement).
The positive association means the barking eventually fades out, as the barking is an emotional response to suddenly seeing a cat.
The long line means you can remove the dog swiftly without chasing or shouting, if the dog is too overwhelmed to take the treats.
Counter conditioning folks - it works, but it is tedious and it does require management too. And not overnight!