Here somebody states:
In um Field Hockey it was 1994 when New Zealand pounded tiny American Samoa 36-1 in an Olympic qualifier. The Samaon goal came when a NZ defender put it in his own net, thus an own goal.
I couldn't verify that.
However, while looking for verification I did find this:
Kookaburras [Australia] slaughter Samoa 26-0 in World Cup qualifier
See here and here.
I assume that this is Samoa, the nation.
And then I found this.
Argentina men 30, Dominican Republic 0
Argentina women 25, Dominican Republic 0
Chile men 25, Dominican Republic 0
United States men 23, Dominican Republic 0
Argentina U-21 women 21, Dominican Republic 0
Chile women 20, Dominican Republic 0
Papua New Guinea (men and women) were beaten with monster scores by New Zealand and Australia, including
New Zealand 39 – 0 Papua New Guinea
And Brazil, Bermuda and Peru have each lost to Argentina with 20 or more goals. See here, here, here.
For other contenders, you might want to check each of these.