I've located two current possibilities in Germany, and one potential option in the United States.

The first, and what looks like the best, option, is a company called Draisinentour. It utilizes sections of the Glan Valley Railway in the German State of Rhineland-Palatinate. It's quite beautiful! The page with pictures of their draisines includes one which has a wheelchair attached:

According to the description:

The barrier-free design is outfitted with two pedal systems and one lever operation, allowing three people on board. The bicycle draisine is registered as a barrier-free operation (Level 1) in compliance with Rhineland-Palatinate Tourism criteria. For more information: www.barrierefrei.rlp-info.de

Clicking on that link leads to a page not found, but that may be because I'm trying to find something in another language. I'd definitely contact them, as that's the only one I've seen that actually has a wheelchair.

The second is Erlebnis Draisine, also in Germany.

Although their pictures don't show it, the page says that wheelchair friendly trolleys are available in their fleet.

They have three routes in the Lengenfeld region of the State of Thuringia. In the descriptions of the first and third, it says

At intervals of 1 to 2 km, there are stops where you can rest and relax. A special draisine with hand drive and wheelchair is available for mobility-impaired guests.

Third, I think an option will be coming soon with Railbikers, in New York and Rhode Island, United States. This is the company I referenced in my answer to this question about railbiking. I sent them an e-mail asking if they had any railbikes that would accommodate wheelchairs, or, if there was an area on the bike to store a folded wheelchair for people who have some mobility but can't be without the wheelchair.

Within twelve hours I received this reply from the owner/managing director.

Unfortunately we don’t have a wheelchair accessible explorer built yet - but we are working with our engineer and designer to fabricate one and hope to have it ready by the end of this year.  However, we have had many wheelchair bound riders enjoy the explorers - with a little help from our friendly staff or family it is very easy to transfer from the wheelchair to the explorer seat. The seats are adjustable and there is ample room to avoid being tangled in the pedals. Every seat has a seat belt and 5 point harnesses are available for younger children or those requiring additional security. While there isn’t really anywhere to stow a folded wheelchair, our staff would be happy to transport the wheelchair to the other end of the ride in one of our vehicles. Please get in touch when making your reservation to let us know of any requests or assistance that you or your group may require. We look forward to rail exploring with you soon!

I thought that was very sweet of them! Since we're intending to visit one of their locations next July, I'll definitely report back as to the status of their equipment.

I've located two current possibilities in Germany, and one potential option in the United States.

The first, and what looks like the best, option, is a company called Draisinentour. It utilizes sections of the Glan Valley Railway in the German State of Rhineland-Palatinate. It's quite beautiful! The page with pictures of their draisines includes one which has a wheelchair attached:

According to the description:

The barrier-free design is outfitted with two pedal systems and one lever operation, allowing three people on board. The bicycle draisine is registered as a barrier-free operation (Level 1) in compliance with Rhineland-Palatinate Tourism criteria. For more information: www.barrierefrei.rlp-info.de

Clicking on that link leads to a page not found, but that may be because I'm trying to find something in another language. I'd definitely contact them, as that's the only one I've seen that actually has a wheelchair.

The second is Erlebnis Draisine, also in Germany.

Although their pictures don't show it, the page says that wheelchair friendly trolleys are available in their fleet.

They have three routes in the Lengenfeld region of the State of Thuringia. In the descriptions of the first and third, it says

At intervals of 1 to 2 km, there are stops where you can rest and relax. A special draisine with hand drive and wheelchair is available for mobility-impaired guests.

Third, I think an option will be coming soon with Railbikers, in New York and Rhode Island, United States. This is the company I referenced in my answer to this question about railbiking. I sent them an e-mail asking if they had any railbikes that would accommodate wheelchairs, or, if there was an area on the bike to store a folded wheelchair for people who have some mobility but can't be without the wheelchair.

Within twelve hours I received this reply from the owner/managing director.

Unfortunately we don’t have a wheelchair accessible explorer built yet - but we are working with our engineer and designer to fabricate one and hope to have it ready by the end of this year.  However, we have had many wheelchair bound riders enjoy the explorers - with a little help from our friendly staff or family it is very easy to transfer from the wheelchair to the explorer seat. The seats are adjustable and there is ample room to avoid being tangled in the pedals. Every seat has a seat belt and 5 point harnesses are available for younger children or those requiring additional security. While there isn’t really anywhere to stow a folded wheelchair, our staff would be happy to transport the wheelchair to the other end of the ride in one of our vehicles. Please get in touch when making your reservation to let us know of any requests or assistance that you or your group may require. We look forward to rail exploring with you soon!

I thought that was very sweet of them! Since we're intending to visit one of their locations next July, I'll definitely report back as to the status of their equipment.