I had a dog bite claim last year and my insurance dropped my coverage.
What kind of dog?
My insurance agent couldn't find a company to insure me
Was that a captive agent at a direct writer or an independent agent? If it wasn't an independent agent I suggest you contact an independent agent that has access to several companies in the high risk market to see if you can get more competitive rates.
It includes dwelling which I don't need because I live in a condo.
Don't think you need property insurance? Well, I've read many tales of woe from condo owners on other sites who thought the same and then suffered tremendous property losses due to water damage, windstorm, fire or theft. You might not think that anything can happen to your personal property but when the storm breaks the windows and the rain comes rushing in or when the upstairs plumbing cuts loose without any fault of the upstairs owner and inundates your unit or a fire destroys your unit and you have no money to live elsewhere or repair the interior damage, you'll think otherwise.
And, with most condos, your "unit" can include structural elements from the floor, ceiling, and wall beams inward. That includes your drywall, paint, cabinets, fixtures, carpet, sometimes the wood flooring. The HOA won't cover any of that.
Does anyone have any experience with this type of situation? I know that my options are few but I want to find condo insurance that can cover me that excludes my dog and dwelling.
You might be able to find a policy that excludes dog liability but you would be foolish to buy one as the dog is your BIGGEST risk for getting sued if the dog bites somebody else. Without liability insurance for that your financial future goes in the toilet if you get sued. Even if, somehow, you are absolved of negligence (though most states have strict liability) you can potentially pay a lawyer tens of thousands of dollars before you are done.
Sorry to have to say this, but you might want to consider giving up the dog.