use the below URL to get the large image:
https://graph.facebook.com/fb_user_id/picture?type=large
For cover image, use the below:
http://graph.facebook.com/fb_user_id?fields=cover
this will return:
{
"cover": {
"id": "XXX",
"source": "cover_image_url",
"offset_y": 66
},
"id": "XXXXXX"
}