The firm, which was established 22 years ago, employed 18 management and staff and ran a workforce of around 80 operatives.
Coalway had expanded in recent years working directly for councils in the Midlands and contractors operating in the region. Most recently is worked for Thomas Vale on a school job in Bilston and with building services contractor Crown House on a programme to upgrade six Wolverhampton secondary schools.
The firm was also working for fit-out specialist Cameron Black, which itself went into administration last week, on a Parliamentary Estate building refit at 53 Parliament Street in London.
Coalway turned over around £10m and had recently spread its geographical base to work on jobs in Northamptonshire, North Staffordshire, North Wales and Winchester.
The Birmingham office of BDO are the administrators.