To make the trigger disappear after you use it, you need to do trigger delete(); or trigger TriggerEnable(false); (True will enable it again.
Also I am not too familar with changing dvars via script on BO3, but to use the cheat via console you need to do /god, so maybe you just need to add the / before god in the script.
trigger = GetEnt("GetGod", "targetname");
trigger SetHintString("Press ^3&&1^7 For GOD MODE");
GodCost = 1000;
trigger waittill("trigger", player);
if(player.score >= GodCost)
trigger PlayLocalSound( "cha_ching" );
ModVar( "god", 1 );
trigger PlayLocalSound ( "deny" );