As I pointed out in a comment, free-market environmentalism is supported by the US Libertarian Party and the UK Libertarian party. So there is one proposal that has some backing from libertarian groups.
Unfortunately I am not aware of any specific proposals being pushed by conservatives parties, so instead, I'll point out a few ideas from conservative and libertarian thinkers that will hopefully shed some light on what sorts of proposals we might expect from these groups. I am going to try to refrain from extrapolating too much and let the ideas speak for themselves.
First, there are some who would argue that democratic, free-market capitalism in and of itself promotes sustainability and that without it sustainability is impossible. So, if you accept this premise, then the best policy that can be pushed to promote sustainability would be free-market capitalism.
Second, I quote from Thomas Sowell's Basic Economics:
While there are many decisions that can be made more efficiently through the marketplace than by government, this [pollution in particular, but generalizes to sustainability practices] is one of those decisions that can be made more efficiently by government than by the marketplace. Clean air laws can reduce harmful emissions by legislation and regulations. Clean water laws and laws against disposing of toxic wastes where they will harm people can likewise force decisions to be made in ways that take into account the external costs that would otherwise be ignored by those transacting in the marketplace.
Third, Milton Friedman.
Finally, I want to point out something about the question as written that I think relates to this discussion and might offer some insight into conservative and libertarian policies. The question deals with "solutions", "One answer points out that it's not the problem identification that is associated with progressive politics, but rather the proposed solutions" and "What solutions have been proposed by conservative, neoconservative or..." Some conservatives and libertarians would argue that there are no solutions to this problem, only trade-offs. For example, Thomas Sowell in The Vision of the Anointed:
Moreover, the available resources are always inadequate to fulfill all the desires of all the people. Thus there are no “solutions”... only trade-offs that still leave many unfulfilled and much unhappiness in the world.
Whether specifically stated or not, I think (no citations here, unfortunately) that many conservatives/libertarians share this belief. Therefore, we can expect conservative/libertarian proposals to attempt to balance these trade-offs incrementally. As Justice Oliver Wendell Holmes put it
to improve conditions of life and the race is the main thing--but how the devil can I tell whether I am not pulling it down more in some other place?"