One of the reasons I love Jane Austen's novels so much is her sarcasm. Here, on the surface, it might seem that the father is criticising Kitty for coughing at inconvenient times. Of course we can't really time our coughs, so the father is actually telling his wife off for being so mean to Kitty. The expression itself "she times them ill" is archaic and not used today, as others have pointed out below. Austen uses the word "ill" several times. One other example is Elizabeth pointing out that someone wrote the address "very ill" on an envelope. We might say "badly" in both these cases now, instead of "ill".

Yes, as Robin says, it means she times them badly, she coughs when it is the worst time to do so. Using ill to mean bad sounds very old fashioned now. It only remains in use in idiomatic phrases, like "ill gotten gains" and "it's an ill wind that blows no good", or saying someone is "ill prepared" for something (unprepared or badly prepared).

She times them badly It's old english, you would never hear ' she times them Ill" in modern speech.

There is a fantastic adaption by the BBC of Pride and Prejudice with Colin Firth and Jennifer Ehle. It was very popular and much loved series, and I highly recommend it. Yes, Austen isn’t modern English but she is a great writer.

It means that she probably sneezes at times that it might considered to be impolite. Of course, she had no control over it, but her bad luck makes her do it at the worst possible times.