Computing a bounding box or averaging the lat-long coordinates will more-or-less work for locations that are not on the 180th meridian; that is, is pretty much anywhere but in Fiji.
An approach that will work anywhere on the globe, Fiji included, is converting the coordinates into points on a 3D sphere, computing the midpoint, and projecting the midpoint to the surface of the sphere. This of course will be computationally more expensive.
First convert each lat-lng pair into 3D cartesian coordinates:
x = cos(lat)*cos(lng)
y = cos(lat)*sin(lng)
z = sin(lat)
Then compute the midpoint by averaging the coordinates, giving (x', y', z')
. Now convert this back into lat-lng, and you'll have the coordinates for the center point:
r = sqrt(x'² + y'² + z'²)
lat' = asin(z'/r)
lng' = atan2(y', x')