I feel that the approach is best tailored to the individual. What sort of a person is your sister? She is evidently a devoted parent so what issues would get most to her, in addition to the birthday?
Refusing a life saving blood transfusion to a dying child?
Being told what toys to allow, or not, to give the child? ( I refer to the video of Caleb and his Sparlock wizard toy)
Being willing to shun a teen child or upward, who has left home and "left Jehovah"
The child abuse problem in their ranks
Accepting a woman's role as subordinate to her "husband as her head".....Whatever will get to her.....
Some people respond to logic and reasoning about failed prophecy, the calculation of dates and times, the assertion that Jerusalem fell in 607 BCE when archaology supports 587 BCE, the frequent miss-quotes in their literature, the UNO scandal..
You can see that there is a great field of various issues. Finding the right one may take some time but your sister and her child must be worth it.