The diagonal relationship between beryllium and aluminum and the isoelectronic relationship between BeH unit and Al atom were utilized to design a new series ppC- or quasi-ppC-containing species C-5v CBe5H5+, C-s CBe5H4, C-2v CBe5H3-, and C-2v CBe5H22- by replacing the Al atoms in previously reported global minima planar pentacoordinate Al to Be-H carbon (ppC) species D-sh CAl5+, C-2v CAl4Be, C-2v CAl3Be2-, and C-2v CAl2Be32- with BeH units. The three-center two-electron (3c-2e) bonds formed between Be and bridging H atoms were crucial for the stabilization of these ppC species. The natural bond orbital (NBO) and adaptive natural density partitioning (AdNDP) analyses revealed that the central ppCs or quasi-ppCs possess the stable eight electron-shell structures. The AdNDP analyses also disclosed that these species are all 6 sigma-2 pi double-aromatic in nature. The aromaticity was proved by the calculated negative nucleus-independent chemical shifts (NICS) values. DFT and high-level CCSD (T) calculations revealed that these ppC- or quasi-ppC species are the global minimum or competitive low-lying local minimum (C-s CBe5H4) on their potential energy surfaces. The Born-Oppenheimer molecular dynamic (BOMD) simulations revealed that the H atoms in C-2v CBe5H3- and C-2v CBe5H22- can easily rotate around the CBe5 cores and the structure of quasi-planar C-5v CBe5H5+ will become the planar structure at room temperature; however, these interesting dynamic behaviors did not indicate the kinetic instability as the basic ppC structures were maintained during the simulations. Therefore, it would be potentially possible to realize these interesting ppC- or quasi-ppc-species in future experiments.