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The event generator BEEC (Yang et al. (2013) [11]) was devoted to the simulation of heavy quarkonium production at an unpolarized electron-positron collider. We upgraded it here by adding the generation of quarkonium with polarized electron and positron beams. In addition, the production of color-singlet 2 S -wave states were included. Several future electron-positron colliders with high luminosity have been under discussion in the past decade. Especially, their possibility of producing polarized beams is important for providing more insights into the underlying physics. This upgraded version offers a useful tool for the feasibility study on quarkonium from the experimental side. Program title: BEEC version 2.0 CPC Library link to program files: https://doi.org/10.17632/bvtwwm22tj.1 Licensing provisions: GNU General Public License 3 Programming language: FORTRAN 77/90 Journal Reference of previous version: Comput. Phys. Commun. 184 (2013) 2848 Does the new version supersede the previous version?: Yes Reasons for the new version: The proposed electron-positron colliders could possibly produce polarized beams, with which it would be helpful to provide more insights into the structure of the underlying physics in heavy quarkonium. Thus, it is essential to simulate the quarkonium production through polarized beams. In addition, the B c (2 S) state attracted more and more interests since its discovery, which makes it necessary to produce the 2 S -wave excited states. Summary of revisions: Two polarized amplitudes of leptonic scattering are computed theoretically. The relevant codes of the formula are included in BEEC2.0. Meanwhile, new parameters for the 2 S -excited states are also included. Nature of problem: Although PYTHIA can generate events for many processes, a dedicated event generator is also necessary. Especially, PYTHIA does not internally produce events with polarized beams. BEEC is implemented into PYTHIA as an external process for simulating heavy quarkonium events with high efficiency. Further hadronization and decay simulation can be done by using PYTHIA subroutine. Solution method: Two projection operators are used to calculate the polarized leptonic scattering amplitudes with the help of improved trace technology [1,2]. The code with option can generate events through unpolarized and polarized initial beams. In addition to the (Q Q ′ ¯)-quarkonium (Q , Q ′ = b , c) in color-singlet 1 S -wave states, 1 P -wave states, and the color-octet 1 S -wave states in the last version, BEEC 2.0 also deal with the production of 2 S -wave excited states within the framework of non-relativistic QCD [3]. Additional comments including restrictions and unusual features: About the running time, it depends on which option one chooses to match PYTHIA when generating the heavy quarkonium events. Typically, for the production of the S -wave quarkonium states, if setting IDWTUP=1 (unweighted events), then it takes about 21 minutes on a 3.22 GHz Apple M1 Pro Processor machine to generate 105 events; if setting IDWTUP=3 (weighted events), it takes only ∼5 minutes to generate 105 events. While for the production of the P -wave quarkonium states, the time will be almost one hundred times longer than the case of the S -wave quarkonium. [ABSTRACT FROM AUTHOR]