When the person on whom the service of the summons in an action for divorce from the bonds of matrimony is to be made cannot, after due diligence, be found within the State and that fact appears to the satisfaction of the court, or judge thereof, the clerk of the court of common pleas, the master or the probate judge of the county in which the cause is pending and it in like manner appears that a cause of action exists against the defendant in respect to whom the service is to be made, such court, judge, clerk, master or judge of probate may grant an order that the service be made by the publication of the summons in the manner and with the effect provided in §§ 15-9-710 to 15-9-740. In lieu of publication of summons as provided in §§ 15-9-710 to 15-9-740 the plaintiff may cause such process to be served personally upon any nonresident and the service so made shall be sufficient.