It is potentially possible to get the visa at the Syrian border. The official rule is that you have to apply in the country where you are resident if that country has a Syrian representative (which I assume Dubai has?), otherwise you can get it at the border.
In Dec 05, I was refused a Syrian visa in both Egypt and Jordan, on the basis that I wasn't a permanent resident there and hadn't applied for the visa in my home country (Australia, where I hadn't lived for several years).
I contacted the Syrian embassy in Australia who in turn apparently contacted the border crossing with Jordan and requested that they grant me a visa on the border. I'm not actually sure if this made the slightest bit of difference, but when I turned up at the border they gave me a visa on the spot without any hassles. I also met an American who turned up without a visa and after camping at the crossing for 24 hours they gave him a visa. Therefore it is possible.........
Good luck
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