Suggest to them it's built into the duties of the publicity chair or something? Or alum chair? Some groups even have a newsletter chair (I'm guessing sometimes those people carry more than one role).
Suggest they make sure all the news that might be of interest to the graduated sisters is fed back so it can be put in the newsletter. Maybe create a template for them or suggest software (e.g. MS Publisher being a simple option); if they don't have DTP skills they might otherwise be scared off by it.
Convey, reassure and reinforce to them when you suggest it that you are interested in hearing about their continued successes, their troubles and their triumphs. Explain the strong bond you still feel toward the chapter and how you understand other alums do too and so want to be kept in the loop so you're equipped with knowledge of the chapter in their hands and as alums can better support them. Indicate though the chapter house (if they had one) isn't home to the alums any longer, home remains where your heart is and that it rests with the suchandsuch chapter of KKG. Well I don't know if any of that helps - if not I'm sure lots of people will have suggestions for you
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Good luck.
As DGMarie said posting it on a website is an excellent idea and keeps costs down. Do a search (in the Lambda Chi Alpha forum) on here too for the word newsletter, they've talked about them a bit and probably have a coupla example links there.