A few US states require or required a supermajority in the legislature to pass the annual budget. The issue is somewhat complicated by the fact that in some states some budgetary items/issues require a supermajority and some don't; at least as of 2015 (for which I found a survey):
States that impose a supermajority requirement to pass the budget do so in a variety of ways. Of the 10 states that have the requirement, only three—Arkansas, Nebraska and Rhode Island—impose it on budgets submitted on time and within expenditure limits. The ways these limits are set vary by state, but can include statutory or constitutional measures or enacted legislation. Others operate along a spectrum, ranging from requiring a supermajority vote for specific types of appropriations to requiring a supermajority to agree on increasing tax and expenditure limits (TELs).
California experienced the most significant change in recent years regarding supermajority requirements for passing the budget. In 2010, voters approved Proposition 25, an initiative that eliminated the two-thirds vote requirement to pass the budget. [...]
Are there any [fully independent--let's say UN recognized, so we don't into an argument about this] countries that have a supermajority provision on the entire budget? Or at least any significant historical examples of countries where this was the case for a substantial amount of time? If not, is there any country where there are substantial per-item/per-issue supermajority budget-approval requirements?