I am guessing you could find a rental in CV that allows dogs. Only because those are high end homes, and I think high end renters may be permitted dogs, as they may be presumed to be more responsible. I concur about checking craigslist and using the pet screening option.
I think it is the lower end homes that won’t allow dogs because they end up with people that don’t take care of the dogs, and the dogs trash the house, left outside tethered on leashes (which is now against the law).
What I would check is if there is any law forbidding bringing pets to USA. Also, you cannot fly with pets during the summer or winter, because large pets are put in the cargo hold, and can die from heat or cold.