The major contractors and some minor contractors do this sort of work. Just so that you know, I am with Jacobs and have also been with most other majors. Consider the majors if you need a new building and may relocate existing DCS or supporting materials; or if you buy a new DCS.
Some DCS manufacturers could contract this work if you plan to replace the DCS etc. Buying a DCS shelter could also be OK. The total scope for a control room might not be a sound path.
A few other vendors that we use can do the relocation work. A few vendors supply buildings and can do the relocation work too. I use ENGlobal and Contech for analyzer shelter work but they may be OK for control room work too. Other suppliers are well knows for rack room equipment, DCS/SIS integration etc.
For you to select the type business really need to clarify your total scope. Do you need a new DCS? How about a new UPS? Is this only an operator control room or does it include both operations and the control system hardware? Do you consider remotely located DCS I/O hardware that communicates with the controller? Much more could be discussed. Some really cool operator lighting schemes exist that you might never imagine. Is this large or small? Will there be a plant shutdown? If so, how long; six weeks, more, less, etc.? Did I fail to mention other key issues such as HVAC, air system environmental protection, etc.? Help clarify the job scope and some can help with a bidder list. if really needed we (and not just me) could discuss or email some details that you don't want to be shown here.