One variation I've heard would be for cities and states to not be allowed to issue debt, that only the federal government could do that. It would mean the local units of government (which actually run and fund most things) would have to operate on a balanced budget, and would provide a lot of robustness in the system relative to what we have now. If they needed a one-time bailout for some reason (natural disaster etc) the federal government could give funds to the local area, potentially issuing debt if necessary.
Of course that doesn't provide any protection against federal debt binging... so I'm not sure how you'd square that. You don't really want to prohibit the federal government from taking on debt - for example, the largest debt the US ever accumulated was to fight and win WW2. But maybe there are strings you can attach.
One such string that makes a lot of sense to me is the idea that you should never allow debt for operating expenses or maintenance. You would think that would be obvious and you wouldn't actually need a policy to enforce that outcome, but unfortunately it's common practice today to just issue bonds if you can't afford to maintain your municipal services.