A Tradable Credit Scheme (TCS) is a demand management policy promoting more sustainable travel behaviors. The regulator defines the credit distribution among the population. It also determines the required credit charges for each travel alternative at different times of the day. The credit price is determined by the trade of credits between travelers. Defining the credit scheme at the urban level and estimating its impacts on user travel decisions and the network congestion dynamics is challenging. We propose a framework wherein travelers change their departure times and choose between solo car driving, Public Transportation (PT), and carpooling to complete their trips under a dynamic TCS, meaning the credit charge is time-dependent. A multimodal macroscopic traffic simulator based on a generalized bathtub model captures the congestion dynamics for the different transport modes. Additionally, we consider different values of time, trip lengths, and desired arrival times. The proposed TCS minimizes the congestion cost and the carbon emissions. The stochastic user equilibrium is computed through an iterative method. The methodology is implemented and applied to a realistic test case in Lyon (France). The dynamic TCS profiles result in up to 20% congestion reduction for 57% fewer carbon emissions.