Techniques to deliver privacy-preserving synthetic datasets take a sensitive dataset as input and produce a similar dataset as output while maintaining differential privacy. These approaches have the potential to improve data sharing and reuse, but they must be accessible to non-experts and tolerant of realistic data. Existing approaches make an implicit assumption that the active domain of the dataset is similar to the global domain, potentially violating differential privacy. In this paper, we present an algorithm for generating differentially private synthetic data over the large, weakly constrained domains we find in realistic open data situations. Our algorithm models the unrepresented domain analytically as a probability distribution to adjust the output and compute noise, avoiding the need to compute the full domain explicitly. We formulate the tradeoff between privacy and utility in terms of a "tolerance for randomness" parameter that does not require users to inspect the data to set. Finally, we show that the algorithm produces sensible results on real datasets.