Correlated paired binary data often arise in biomedical studies involving paired organs, where each subject may contribute zero, one, or two positive responses. This paper considers simultaneous confidence interval construction for many-to-one comparisons of proportion differences between several comparison groups and a common control. Existing methods, including method of variance estimates recovery (MOVER), Wald-type, profile likelihood, score, and Normal-Dunnett procedures, mainly rely on first-order normal or chi-square approximations, whose finite-sample accuracy may be affected by sparse counts, unbalanced designs, strong within-subject dependence, or an increasing number of groups. We propose a Dunnett-type saddlepoint simultaneous confidence interval method under the constant- $R$ model. By using the three-category structure of paired binary responses, the cumulant generating function of the treatment-control contrast vector is derived explicitly and used for saddlepoint calibration of the joint distribution. Simulation studies show that the proposed method improves simultaneous coverage accuracy in sparse and strongly dependent settings, while remaining comparable to existing methods in moderate settings. A retinitis pigmentosa dataset is analyzed to illustrate the proposed procedure.