Is there anything like "green bonds" for x-risk mitigation?

That's a very interesting idea. Some relevant bits from the linked paper:

Only a few national governments could borrow on reasonable terms at this very long maturity. This observation argues for the creation of credible international institutions to underwrite the issuance of this type of debt. Let us call the prospective institutions the ’World Climate Bank’ or WCB. How could this bank be governed, and how could it maintain its solvency, solidity and credibility for the required period?

In order to pay the interest on the bonds, the WCB would have to command regular revenues. Two possibilities come to mind. The first is that the WCB would receive the proceeds of a global carbon tax directly, or have a first claim on them. [...]

The second is that the WCB could claim a share of national government revenues up to some limit that would allow it to pay interest on the appropriate quantity of debt, even as the revenues from the carbon tax or royalties decline with the declining use of fossil fuel. By this means, the WCB’s source of revenue would be spread across many national governments, thereby increasing the credibility of the interest guarantees in the bonds.

[...]

One risk the holders of WCB bonds would take is that individual nations might withdraw from the bank for some reason, leaving it insufficiently funded to meet its commitments. This consideration suggests that membership in the WCB should be a precondition for membership in other international organizations such as the World Trade Organization, the IMF and the World Bank. There would then be strong incentives for individual nations not to withdraw from the WCB.

[...]

If the WCB indexed long maturity bonds were widely held as international reserves, they would likely become a vehicle for private reserves seeking very low-risk havens, which would contribute to their marketability.