A set of Keplerian and non-Keplerian fits to the orbits of 45 individual TNO binaries. We provide full MCMC chains of our fits, as well as all diagnostics and outputs. We have verified that all Keplerian fits are converged. Non-Keplerian fits are not converged in almost all cases, but were run for a set amount of steps to try and identify targets for longer, converged analyses. A full paper about these fits and a discussion of their implications will soon be submitted to the Planetary Science Journal (PSJ). We provide these fits to allow anyone to fully examine the outputs of our fitting process. They can also be used a starting point for future analyses as the MCMC chains contain a full posterior distribution of the orbital properties of each TNO binary. A readme is contained within the dataset describing the outputs and the use of the MCMC chains. For any further assistance, please contact us. A "frozen" version of MultiMoon compatible with the dataset is also included.