"have no discretion in... " "to have discretion" in this case means to have a choice. This simply means she does not have a choice about when or whether she is going to cough. "She times them ill" "Ill" = ILL in this case means "badly". Meaning she coughs at times when it would be better not to. Perhaps she is disturbing someone by coughing. This is pretty old-fashioned. A modern American might say, "Kitty has no choice about when she will cough. She times her coughs badly." It has been many years since I read "Pride and Prejudice". It is not easy reading, even for a native speaker.

She has no plan to cough. She coughs when she needs to. Kitty's father suggesting this i think so. Time them ill = She doesn't has proper planning about something.