If the output is intended to be used in serial algorithm (not needing a different array for each call), then by not creating a new array every time, you can compute it faster:
function initTileNear(){
    var out = new Array(8);
    for(var i=0;i<8;i++)
        out[i]=[0,0];
    return out;
}
var arr = initTileNear();
function getTileNear(x,y){
  var ctr=0;
    for(var j=0;j<=1;j++)
      for(var i=-1;i<=1;i++)
        if(!(i===0 && j===0))
        {
          arr[ctr][0]=x+i;
          arr[ctr][1]=y+j;
          ctr++;
        } 
    return arr;
}
for(var i=0;i<500;i++)
{
   var test = getTileNear(i*2,i*2+1);
}
this is 300% faster than the original version that re-creates new array everytime.
With a bit longer code, it gets faster:
function initTileNear(){
    var out = new Array(8);
    for(var i=0;i<8;i++)
        out[i]=[0,0];
    return out;
}
var arr = initTileNear();
function getTileNear(x,y){
    arr[0][0]=x-1;
    arr[0][1]=y-1;
    arr[1][0]=x;
    arr[1][1]=y-1;
    arr[2][0]=x+1;
    arr[2][1]=y-1;
    arr[3][0]=x-1;
    arr[3][1]=y;
    arr[4][0]=x+1;
    arr[4][1]=y;
    arr[5][0]=x-1;
    arr[5][1]=y+1;
    arr[6][0]=x;
    arr[6][1]=y+1;                            
    arr[7][0]=x+1;
    arr[7][1]=y+1;                                
    return arr;
}
for(var i=0;i<500;i++)
{
   var test = getTileNear(i*2,i*2+1);
}
If indices are 32-bit, then this is 400% faster:
function initTileNear(){
    var out = new Array(8);
    for(var i=0;i<8;i++)
        {
            out[i]=new Uint32Array(2);
            out[i][0]=0;
            out[i][1]=0;
        }
        
    return out;
}
var arr = initTileNear();
function getTileNear(x,y){
    arr[0][0]=x-1;
    arr[0][1]=y-1;
    arr[1][0]=x;
    arr[1][1]=y-1;
    arr[2][0]=x+1;
    arr[2][1]=y-1;
    arr[3][0]=x-1;
    arr[3][1]=y;
    arr[4][0]=x+1;
    arr[4][1]=y;
    arr[5][0]=x-1;
    arr[5][1]=y+1;
    arr[6][0]=x;
    arr[6][1]=y+1;                            
    arr[7][0]=x+1;
    arr[7][1]=y+1;                                
    return arr;
}
for(var i=0;i<500;i++)
{
   var test = getTileNear(i*2,i*2+1);
}
If you can use single-dimension, it is 10x faster:
function index(y,x)
{
    return x+y*2;
}
function initTileNear(){
    var out = new Uint32Array(16);
    for(var j=0;j<8;j++)
    for(var i=0;i<2;i++)
        out[index(j,i)]=0;
        
    return out;
}
var arr = initTileNear();
function getTileNear(x,y){
    arr[0]=x-1;
    arr[1]=y-1;
    arr[2]=x;
    arr[3]=y-1;
    arr[4]=x+1;
    arr[5]=y-1;
    arr[6]=x-1;
    arr[7]=y;
    arr[8]=x+1;
    arr[9]=y;
    arr[10]=x-1;
    arr[11]=y+1;
    arr[12]=x;
    arr[13]=y+1;                            
    arr[14]=x+1;
    arr[15]=y+1;                                
    return arr;
}
for(var i=0;i<500;i++)
{
   var test = getTileNear(i*2,i*2+1);
}