Solutions (so sensible that they are guaranteed political suicide):
1. A carbon tax, starting off modest, but with a growth escalator built in and known in advance to assist planning of transition.
Note: Since we know the economy did ok with oil priced double what it is now, the carbon tax need not start out so modest. It could be adaptive, so that for example retail gasoline prices are made roughly what they just were over the last 5 years (average), as a starting point for the tax to kick off system-transition investments.
Carbon trading is not a viable option. A simple at-source carbon tax is more effective and more transparent. Carbon trading is too easily gamed by accountants at the expense of physical reality. e.g. giving you credit for the forest you haven't chopped down yet (how nice of you) so that I can continue to burn more coal.
2.One third of proceeds of carbon tax used to reduce income tax, to keep the economy stimulated.
3. One third of carbon tax revenue used to fund R&D into bleeding-edge alternative energy and transportation technologies.
e.g. better PV, better batteries, hyperloop, magnetized target fusion, thorium, novel grid-scale energy storage, smart-grid, superconducting supergrid
4. One third of carbon tax revenue used to fund non-fossil-fuel infrastructure projects with current technology. Examples:
a) Rapid transit
b) High-speed rail links
c) Energy-efficient building technology (LEED, Passivhaus) - regulations for all new construction, and subsidies
d) Geothermal Energy Projects. Redirect oil&gas industry drilling know-how and workers.
e) Significant feed-in tariffs for clean renewables (as done previously in Germany)
f) Other incentives for solar farms and solar thermal plants with molten-salt energy storage
f) Other incentives for residential PV and solar water heating
g) Deployment of grid-scale storage initially using existing technologies including Li-ion and sodium sulphur batteries, pumped hydro, underground pumped hydro.
h) Addition of long-distance HVDC power transmission lines long enough to cross weather systems. Encourages wind power and solar by evening out intermittency.
i) Expanded subsidy of electric vehicle purchase.
j) Electric vehicle charging infrastructure expansion