product available on request (or: on demand)?
Solution 1:
Both are perfectly correct. However, a customer's wish to buy a product is usually referred to as demand, which makes me think that demand is more appropriate when talking about products in a store or so.
When talking about information (This information is available on request/demand), I'd use request, for the same reason: information is never demanded by a customer; it is requested.
Solution 2:
Both make good logical sense.
"On demand" though has three specific meanings when it comes to providing goods:
That a token or voucher indicates you have a right to something (as with promissory notes, with some paper currencies operating as such).
That a company keeps a deliberately-low inventory of the product (if a retail company) or the materials (if a manufacturer), and obtains it as needed.
That what is provided is either digital goods (software, MP3s, electronic books) or a service which is made available immediately upon request.
The third is really the second applied to non-physical items, but to the customer the third tends to always reduce delays (a server or process can provide what they purchase in seconds) while the second can both decrease delays (by making a large range available without a "special" order being required) and increase delays (because there are no items yet in stock) compared to other approaches.
I'd favour on demand when it fits one of those models cleanly.
If it doesn't then I'd favour "on demand" for services and information goods if they are provided immediately (within seconds) because as far as the customer is concerned, that's what they are used to when they hear such a service is "on demand". However, with an information product that is available for free to someone who has already paid for something, I'd always use "on request" for as that's a common use (e.g. if manuals or documentation or software isn't included with a product, but you will provide them to customers who ask for them without an extra charge).
Otherwise I'd favour "on request" to avoid being confused with those other senses of "on demand", especially since it is quite a buzz phrase at the moment.