The party said temporary halts would help make the case for permanent new stations.
Its MSPs are lobbying Scottish Government officials to consider the novel approach as part of a deal struck in return for supporting the minority SNP’s 2018-19 budget.
Finance secretary Derek Mackay has agreed to consider a new “pipeline” fund of up to £2 million to develop new stations and lines.
It was prompted by the Greens’ concern that no new rail projects have been proposed by Scottish Government agency Transport Scotland since it was created 12 years ago.
New stations on existing lines which have opened since 2006, such as Edinburgh Gateway and Laurencekirk, had been previously approved.
Consultants Allan Rail, run by former Transport Scotland rail official David Prescott, have suggested around 20 possible pop-up station sites across Scotland.
They are in addition to plans already being considered for stations at Beattock, Eastriggs and Thornhill in Dumfries and Galloway.
Other possible candidates include Dunragit or Glenluce on the Stranraer line, and on the lines east of Inverness.
Allan Rail has also proposed re-opening of the Dyce-Ellon line in Aberdeenshire, the Alloa-Dunfermline line, and branches to St Andrews and Levenmouth.
It said the Larkhall line could be extended to Stonehouse and Strathaven in South Lanarkshire.
Network Rail built a £300,000 temporary station in six days in Workington after the Cumbria floods in 2009 split the town in two.
It was constructed using scaffolding and planks, with a portable waiting room and gravel car park.
Conon Bridge in the Highlands, which opened in 2013 as one of Scotland’s smallest new stations, cost twice as much.
A temporary station was also built at Meadowbank Stadium in Edinburgh for the Commonwealth Games in 1986.
Scottish Greens environment spokesman Mark Ruskell said: “Pop-up stations would be another step towards reversing the legacy of the transport policies of the 1960s when rail lines were ripped up and the car was king.
“They would enable market testing of new stations and allow more robust business cases to be developed.
“It takes a long time for an idea to turn into a proposal, and for appraisals and feasibility studies to be approved.
”Local communities can now put their proposals forward, and temporary stations would be one of many practical options to progress ideas.”
Rail use in Scotland is at record levels, with underlying passenger growth over more than a decade pushing total annual journeys to almost 100 million.
New ScotRail trains this year will also significantly boost the number of services run.
A spokesperson for campaigners Railfuture said: “Although Scotland has seen many more reopenings than England in the last few years, getting any sort of new rail project off the ground is still frustratingly expensive and bureaucratic, so we welcome any moves to kick-start and ease this process.
“Network Rail has shown how it’s possible to open temporary stations at short notice, so it makes sense to try using pop-up stations to test demand.
“There are numerous examples in other industries of new products and services being test-driven, so why should the railways be any different?”
However, a rail industry source said: “£2m is not a lot of money if you want to open stations.
“Money would probably be best used helping local authorities and other groups on developing conventional business cases for stations.”
A Transport Scotland spokesperson said: “We are supportive of the development of new and innovative initiatives which deliver benefits for passengers, freight customers and local communities. We are aware of this proposal and are giving it consideration.”