This puzzle is from the excellent book The hidden mathematics of sport by Rob Eastaway and John Haigh, reproduced here with kind permission of the authors.

Solution to first puzzle:
United beat City 1-0
United drew with Albion 0-0
City beat Albion 2-0

Solution to second puzzle:
Athletic beat Town 1-0
Athletic beat Wanderers 3-1
Rovers beat Athletic 3-0
Town beat Wanderers 1-0