theobservantone tell your SIL you are very sorry but no way can your niece come to this event. She has chicken pox and needs to stay away from this event. Your son has not had chicken pox yet. End of.
"Now I know chicken pox isn't a particularly big deal... "
Actually chicken pox can be a big deal and in a very few cases can be fatal, which is why some parents choose to vaccinate their children against it.
You can get t more than once so even if you and others have had it, you could get it again.
"Everyone gets it and it's part of childhood." Not so, some people do not, and people who are vaccinated against it, with the required number of shots are much, much less likely to ever get it.
"But the trouble is my DS has been so poorly recently with cold after cold and a lingering chesty cough for almost a month which is only now starting to clear." Then please protect your son and put him first.
"I would hate the thought of him suffering with chicken pox when I'm not there to comfort him." Then do not put him in harms way or allow any family member to try and convince you to do so.
"So the predicament is that sister in law and family cannot get childcare for niece, and will miss the sporting event if they cannot all stay with us." This is not a predicament exactly, it is just a fact.
(predicament - a difficult, unpleasant, or embarrassing situation).
It is not embarrassing for you to put your child first and it is certainly not unpleasant or difficult. We are talking about your own son in his own home.
"I feel so awful at saying niece can't stay and sister in law has just text to say she's in tears and so upset." Very sad she is upset but as I say it is a fact, she is ill. When ill we cannot risk infecting other people simply because it is upsetting. Be kind and pleasant but firm. No way, and frankly if your SIL, seeing her sick child, is willing to run the risk of infecting your son, she is being extremely selfish.
Sorry, but please be firm.