I'm a Sr Manager, and I made the request to my manager (Dir) and skip (Sr. Dir) for access to their respective calendars after sharing mine with them and both refused. They claimed that they had meetings on their calendars that cover topics they shouldn't give visibility to. What's an effective response to change their mind, or an alternative option to get at least some visibility to their meetings? TIA.

Which direction we talking about here?
If they're your direct and one of his directs: raise eyebrow and ask again. Perhaps explain briefly eg there's some specific spot-checking you're doing across your directs to ensure consistency in evaluating work performance. Decide whether to address whatever's going on outside of your view. And show them a tactic or two on blocking out time on their calendars while not revealing topics, if you're feeling kind.
If you report to them: apologize and back off. They have calendared work which is (by definition) above your pay-grade they feel you don't need to know about. Figure out what you need that calendar access would have given -- try to get that. Maybe an assistant can hint you about their preferred meetings times?
In reply to Which direction we talking about here? by Joseph Beckenbach
Swimming Upstream - Your Boss's Calendar
I report to them. I'm trying to follow the guidance in the recent Swimming upstream cast. Neither have assistants, so that's not a viable alternate avenue. Calendar access would give me visibility to meetings they have that impact my team's responsibilities. It'd also help me be prepared for seemingly random requests, the cadence of periodic requests, and give some visibility to topics of discussion in which I'm not currently included.
In reply to Swimming Upstream - Your Boss's Calendar by Shaw Strothers
Time to find alternatives
If you've got stable one-on-ones with your boss, that's an ideal venue for finding out about such meetings and their results. Staff meetings with your boss and peers might also serve.
Lacking one-on-ones, regular professional updates (which you drive) might let you gather the info you want. https://www.manager-tools.com/2008/11/boss-one-on-ones-professional-upd…