Technically speaking, many other cryptocoins are based off of the source code of Bitcoin. However, a quick look at the Anoncoin website (https://anoncoin.net//) suggests that it's been heavily modified from that of Bitcoin (using the darknet, i2p, and all that). Therefore, an API that works with Bitcoin, such as those at inputs.io or blockchain.info is really unlikely to work with Anoncoin in particular. On a more specific note, Anoncoin is a Scrypt-based cryptocurrency, while Bitcoin is SHA-256 based. Therefore, they're even less likely to be able to use the same API. Even if you did try to perform operations on Anoncoin (or any other lesser known cryptocurrency) with the API of a Scrypt-based coin, you're pretty much doomed to fail, and if the API doesn't catch that and the coin does make it into the system, then things could get very strange on the server side regarding how the server should process your request.
In conclusion, most cryptocurrencies, if not all (there are so many that I cannot make a giant umbrella statement here) are handled by their own API depending on the website (for example, inputs.io and blockchain.info use two completely different APIs). It also means that lesser known coins will have difficulty gaining support and usability.
Of course, given that Anoncoin doesn't seem to have a notable exchange to support it yet, perhaps you could make your own API, website, or exchange to handle transactions with it to say other cryptocurrencies. Otherwise, it might just be smartest to sit back, wait, and hope for someone else to do it.