Am I able to obtain an injunction against a person to stop them from continuing to defame me?

Maybe, to a limited extent, and likely only after it has been determined that the speech is in fact defamatory.  Keep in mind, we are discussing a different type of relief than what one can obtain through typical restraining and harassment protection orders under Mass. Gen. Laws c. 209A and c. 258E.  What we are discussing is the availability of an injunction against speech to be effective following a finding of defamation.

An injunction to prevent a future defamation has historically not been available as it has been construed as an unconstitutional restraint on speech that violates the First Amendment.  Erwin Chemerinsky, Injunctions in Defamation Cases, 57 Syracuse L. Rev. 157 (2007).  And there continues to be the strong argument that injunctions, even following a finding of defamation, should never be awarded.  Id. at 158.

However, there has been a certain shift towards allowing injunctions in certain situations and to a limited extent.  See e.g. San Antonio Cmty. Hosp. v. S. Cal. Dist. Council of Carpenters, 125 F. 3d 1230, (9th Cir. 1997); Brown v. Petrolite Corp., 965 F.2d 38 (5th Cir. 1992); Lothschuetz v. Carpenter, 898 F.2d 1200 (6th Cir. 1990); Advanced Training Sys. Inc. v. Caswell Equip Co., 353 N.W. 2d 1 (Minn. 1984); Retail Credit Co. v. Russell, 218 S.E. 2d 54 (Ga. 1975); O’Brien v. Univ Comty. Tenants Union, Inc., 327 N.E. 2d 753 (Ohio 1975).  In the civil context, one argument is that an injunction may be available to prohibit speech already determined to be defamatory, thus, the argument goes, we know it is defamatory so it does not enjoy First Amendment protection.  David S. Ardia, Freedom of Speech, Defamation, and Injunctions, 55 Wm. & Mary L. Rev. 1, 67-68 (2013), https://scholarship.law.wm.edu/wmlr/vol55/iss1/2.  This argument appears promising.  Suffice it to say, the issue is debatable and it will take a compelling argument to be successful in obtaining an injunction to prohibit future speech.

In you are suffering from the defamation on-line or in other contexts and you want it to stop, a limited and narrowly tailored injunction may be possible.  One should also keep in mind that traditionally money damages can be awarded to remedy the harm done.

In the event that you are considering taking action to address defamation aimed at you or you are being accused of defamation you believe is justified, feel free to give the author a call.