I have answered on a similar situation here (my co-worker died). Since you worked there, then you should add it on the list of the places you've worked on. I cannot see any other feasible alternative like introduce a gap while you were employed.
You should describe that the company is not trading explaining that you can supply proof that you were there such as payslips, bank account extracts for payments, co-worker contacts etc.
This has happened to me: I was able to locate my ex-CEO from linked-in. He has signed a letter describing my time there and his contact details. I attach it in job applications.
Since there is a lot of mobility in the software industry, I would advise (for the future) to get into the habit of collecting related material as soon as you go. After that you could have it in your own domain/github/dropbox for people in the future. For example after giving your notice to that company, you could have requested a letter about your time there, tasks and employment or a reference letter from a manager. Then you could have it ready for situations like this. Unfortunately software developers unlike say graphic designers cannot have a portfolio to "carry" with them between jobs/clients. Another idea would be to get screenshots of emails for being congratulated, finishing projects etc. Prevention VS cure.