Constant-weight and constant-charge binary sequences with constrained run length of zeros are introduced. The weight and charge distribution for these sequences are found. Next, recurrent and direct formulas for calculating the number of these sequences are obtained. By considering these numbers of constant-weight and constant-charge run-length limited (RLL) sequences as coefficients of convergent power series, generating functions are derived. The fact that generating function for enumerating constant-charge RLL sequences does not have a closed form is proved. Subsequently, implementation of encoding and decoding procedures using Cover's enumerative scheme is shown. Based on the obtained results, some examples, such as enumeration of running-digital sum (RDS) constrained RLL sequences or peak-shifts control capability are also provided.