What NOT to do? I believe what you should not do is approach this niche with an impersonal marketing bludgeon, that is to say you place ads in construction journals or publications, add the words "construction firms" in your laundry list of segments served in your materials and web site, send out a press release, and otherwise dispassionately inform the niche of your presence.
Instead, I recommend the professional(s) in your firm who wish to seek business in this segment become personally involved in approaching the market. Typically, this means they, e.g. get involved with constrtuction-related groups, create a newsletter/blog specifically addressing the market, write and submit articles related to the niche, make themselves available for niche-related speaking engagements, seek out relationships with lawyers and consultants involved in the niche, assemble and conduct a financial/tax symposium focused upon construction issues, and otherwise build a footprint within the prospect population that is based upon personally engaging with prospective clients.
An approach based upon personal involvement will be less expensive and more effective in both the short and long terms in attracting more business from this niche.
One caveat is, of course, that there needs to be one or more partners who enthusiastically involve themselves in the effort. The reality is that sometimes this isn't the case. Finally, there must be appropriate staff and/or vendor support to create marketing materials, track metrics, handle IT issues, follow up, etc.