Some sources suggest painting busbars black to increase the current rating. Is this a good idea?

No. Black matt surfaces are better at radiating heat than bright shiny surfaces, and that is why painting is sometimes suggested. The efficacy of radiation is the emissivity of the surface; for a perfect radiator (matt black), the emissivity is 1 and for a perfect reflector, emissivity is zero. In practice, bright shiny copper has an emissivity of about 0.3, dull copper is about 0.7 and darkened copper – such as a busbar after a few weeks of service – can reach 0.9. Since only around 10-20% of heat is lost by radiation, the difference between dull copper and a matt black surface is only 3-6% of the total.  To achieve this apparent improvement, the 90% of the heat that escapes by convection has to pass through the thermal insulation provided by the paint layer, so the temperature of the bar increases rather than decreases.