Yugoslavia was among the earliest but not the 2nd. Here are the first 10, with dates.
India, Dec 6, 1971 - absolutely no surprise as to who was first
Bhutan, Dec 7, 1971 - not surprising; Bhutan's foreign policy at that time was dictated by India
Poland, Jan 12, 1972 - not surprising; Soviet block
Bulgaria, Jan 12 1972 - not surprising; Soviet block
Myanmar Jan 13, 1972 - surprising
Nepal - 16 Jan, 1972 - not surprising
Barbados - 20 Jan, 1971 - interesting
Yugoslavia - 22 Jan, 1972 - not surprising; Nonaligned movement, Tito was BFF with Indira
The rest 20 or so, in chronological order:
Tonga
Russia
Czechoslovakia
Cyprus
Hungary
Australia
Fiji
New Zealand
Senegal
Britain
West Germany
Finland
Denmark
Sweden
Norway
Iceland
Israel
Japan
Luxemburg
Netherlands
Belgium
Ireland
Italy
src:
http://www.bcstest.com/bdesh_details.php?id=39