There are several layers to this. The first is, have a product people want. The only way to get people to buy a product they don't intuitively want, is to spend a lot of money on marketing in order to make them start to want it. That is clearly not where you are at, at this point.
So for example, if this is a t-shirt you should not have a t-shirt design that is simply your site's logo unless your site is already well established and people want to advertise that they like your site.
A much better shirt would be one that relates to your site, but makes a joke that anyone will understand. Or has a character that is very cute. Or something very witty. Whatever you want to sell has to be naturally desirable enough that people will at least be willing to go through the hassle of ordering and give up at least some of their spare/excess money for it.
Since we just mentioned it, make it extremely easy for people to actually buy your product. Don't make them have to create an account. Don't make them have to go to a different web page. Don't make them have to fill out forms. Use existing systems to minimize all of this.
Finally, associate your product with fun. Don't bring people down (at least not directly) by saying "I have all this product and I'm going to go broke if you don't buy it." Instead (i.e. if it's a t-shirt again), get a photo of a good looking person playing soccer in it. And say something like "Our new t-shirt now available. Lookin' good for $18.99!"
If this doesn't work, consider indirectly going with the "help, I'm going to go broke" method. If you think users value the site you could post saying, "I love this site and our community, but we are running out of funding. Please consider donating to keep the site alive, or buy one of our awesome t-shirts to support us and look good doing it."