SHJ,
India's relationship with the USA was "frosty" during the 60s thru the 80s and only started thawing in the 90s. Air India had a huge spares holding of Super Connie spares and thats what was used by the IAF and IN.
Even the C-119 shared an engine with the Super Connie (Wright 3350s).
Since these were also not combat aircraft (India has not had a US made combat aircraft since the Vultee Vengeance in WWII), their spares availability was not as critical.
Since the major combat aircraft were all either British (Hunter/Canberra/Sea King/Sea Hawk) or French (Mystere/Alize) a courier to the UK would satisfy those needs. An-12s always did the couriers to Russia (Mig-21/Su-7/Mi-8 spares).
As far as I know, there have never been any couriers run by the IAF to the US. Commercial air (Air India) was probably used, Air India had a number of 707 and DC-8 freighters.