This is a surprisingly involved question! The structure of the SiO32- ion is not analogous to that of carbonate ion, CO32-, where you have three resonance structures each with one C=O double bond, giving an average bond order of 1 1/3. Silicon as a rule does not form pi-bonds in this fashion. In fact, the simple ion SiO32- is unknown, just as molecular "SiO2" (analogous to CO2) is unknown; silicon oxides such as quartz and silicates actually occur in more complex structures in which each silicon has four oxygens bound to it in a tetrahedral geometry. These tetrahedra link together in chains (as in pyroxene, ((SiO32-)n, "chain silicate"), in rings ((SiO32-)n where n = 3 or 6), in sheets (in micas), and in three-dimensional "framework minerals".
I would first consider the Si-O bonds to be simple single bonds (bond order = 1), but it is known that in some cases there is some double bond character due to silicon 3d-orbital overlap with the oxygen 2p orbital (dp-pp bonding), but this is not the same as a C=O double bond which is a classic pi-bond made from side-to-side overlap of 2p orbitals from each atom (pp-pp bonding). Thus, in actual silicates, it is probably more accurate to describe the Si-O bonds as single bonds, but acknowledging that there may be a dp-pp contribution.
Steve