They want to reinstate Upton and North Elmsall Station near Wakefield, which was once a stop on the Hull and Barnsley Railway and closed in 1959.
The line, which was built to transport coal to Hull's docks, ran through what is now Upton Country Park, and the group plan to lay a single track across the original route.
They intend to apply for a National Lottery Heritage Fund grant to bring the project to fruition.
A replica of the station would be built on the site of the demolished railway buildings, with part of it used as an information centre and cafe. There would also be displays about Upton Colliery, which was served by the line.
The two-and-a-half-mile track would continue through the old colliery site and through Barnsdale Tunnel, which remains in good condition despite having been disused since 1959. It would terminate just before the A1 at Barnsdale Bar.
Members also plan to lay a footpath and cycleway alongside the rails.
If opened, the heritage railway would hold 1940s and World War One-themed weekends, Santa's grotto experiences, Polar Express trips, Halloween and Easter events, Victorian weekends and driver experience days.
Keith Taylor, 43, started the group and hopes to win support from Wakefield Council, who own the land the trackbed passes through.
He believes the project would meet the main criteria for National Lottery Heritage Fund cash, as it would both restore lost history and benefit the local economy.
"I think Upton is the perfect place for a new heritage railway. The land is owned by the council, so it would be easier to negotiate a lease. At the moment, there are nearly 80 of us - we're just a group of enthusiasts, we don't have a lot of expertise or experience of working on the railways.
"There is a small line at the National Coal Mining Museum, but no others in the Wakefield area. It would be unique as I don't think a heritage railway has rebuilt a replica station from scratch before.
"I'd expect it to cost several million - we've approached an architect for some advice, and we're looking into what grants are available. I think after coronavirus, the government may want to support projects that provide employment. It would restore heritage and stimulate the economy."
The railway would be staffed mainly by volunteers, whose work would range from clearing undergrowth from the old station to operating a steam train along a short stretch of line.
They would have to lease a locomotive and rolling stock from another heritage railway, but hope to secure the use of an original Hull and Barnsley Railway carriage currently owned by a Hull-based preservation society.
The eventual fate of Upton and North Elmsall Station is shrouded in mystery. The Hull and Barnsley Railway was primarily conceived as a goods line to handle the lucrative coal traffic between the South Yorkshire seam and the port of Hull. In order to receive parliamentary approval back in 1885, the company had to commit to providing stations serving communities along the way.
A large number of small halts were built, but the unprofitable passenger service lasted just 40 years and the line did not even reach Barnsley, terminating instead at Cudworth, a few miles short of the town and in the heart of pit country. By 1932, passenger trains no longer called at Upton and the route had become freight-only by the 1950s.
The station closed completely in 1959, and the line was lifted in the early 1960s, after the closure of Upton Colliery. Today, the only surviving section is a short stretch serving Drax power station.
Yet there is no record of its demolition and Keith has struggled to find out more about the end of its operational life.
"We just don't know when it was demolished - it's a real mystery. It once had canopies and waiting rooms, and the stationmaster's house is still there. It was so close to the coal mine that probably nobody wanted to live there, and this was before converting old stations into houses became popular. I imagine it was vandalised at some point and the council had to pull it down.
"Some of the other stations along the line are houses now and have been preserved - we're going to visit Little Weighton soon to get an idea of the interiors, as they were mostly identical to each other.
"There is some of the platform still left, but it's in a poor state of repair and we'll probably have to replace it with a modern platform. The rest of the site is just an overgrown, wooded area, with enough room for engine sheds and a car park."
The trackbed is in good condition, although Keith fears the most costly part of the scheme would be replacing the bridges that were removed in the 1960s.
Barnsdale Tunnel is home to protected species of bat, which could present obstacles, and if plans to widen the A1 go ahead it would mean there would be little space for a halt at this end of the track.
"It wouldn't be a massive issue if we couldn't go through the tunnel, as there were so many spurs to the different collieries that we could use these instead and have a reversal junction.
"We'll approach the council when we've prepared a fully costed plan. I think they would support us - they are keen to promote heritage projects. It will take us around two years to get the survey and planning permission completed.
"I think we could aim to be as popular with visitors as the Keighley and Worth Valley Railway - it would be great to be even partially as successful.
"I'm not a railway expert, but just somebody who loves the design of old stations and the romance of them."
To join the Upton and North Elmsall Railway's Facebook group, click here.