The only fuels that I know are delivered in the small volumes common to residential and small business use are LNG, propane, fuel oil and diesel. Both LNG and propane suppliers typically loan you the tank/s for a nominal fee as long as you keep buying their product. and running out is usually when they suggest a larger, or more, tanks.

Fuel oil and diesel tanks are yours. And yours to figure out how much you need.

I can. offhand, remember any of the fuel suppliers making off hour deliveries unless it was prearranged and agreed to well in advance. Even this was something of a personal favor. I've never heard of an 'emergency' after-hour delivery. Most of those shops run 9 to 5 and shut down completely after that. They do run later in the late fall to cover the large numbers of orders that come but I don't think they even take orders after the office closes.

All I can suggest is to invest in larger tanks to get you into regular working hours. At least an extra 24 hours sounds right to give them time to receive the order and make delivery.

The few cases where a commercial setup needed fuel on short notice we went to the fuel depot, kept open as a personal favor, and hauled 100 pound propane tanks out to the site. Once we had a diesel generator and we got diesel from a local retail gas station, hauled them to the site and refueled by hand. I don't see why this couldn't be done using retail propane suppliers and pre-filled twenty pound tanks. Of course all that depends on a retail supplier being open.

Planning ahead and having adequate tank space to get you through the rough spots sounds like the best way to go.