I think a China-India alliance will soon be a reality, and the US will have to just start living with that! China and India have far more in commen then they have with the US!
A China and India alliance in the near term is highly unlikely due the following reasons: border dispute, China-Pakistan relationship, India-US relationship, and more cultural and information exchange between the countries is need.
The trade between India and China had increased dramatically and will continue to increase. China-India relations had warm up also, even leaders from both countries pledge bilateral ties and cooperation, but that is far from forming an alliance.
In order for even the idea of a China-India alliance to exist, there are issues needed to be resolved before the possibility of an alliance.
First the border dispute, until China and India have agreed on the border, an alliance is unlikely.
Second, China’s support of India’s arch enemy: Pakistan. Therefore, China needs to pay more attention when selling weapons to Pakistan and other military action. India and Pakistan’s problem will persist until the Kashmir situation is resolved to both countries’ satisfaction. Eventhough, Pakistan-India relations had been much better and the term "peach" was even quoted. But the Kashmir situation is far from being resolved.
Third, India needs to distant itself from the US in term of military ties. India has to made clear and through actions that it is only purchasing military hardware from the US and not intended to become another US ally like Japan West of China.
Fourth, there need to a lot of cultural, science, technology, and information exchange between the two countries. Basically, get to know each other better.
In the short term (5 to 10 years), I do not foresee China and India forming an alliance.