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Plastics, Fiberglass or glass-lined steel are most commonly used for service which comes into contact with sulfuric acid. Those choices are temperature dependant. CS can be used if the acid is not dilute (98%), but even atmospheric moisture can dissolve into the acid over time causing it to become more dilute and result in corrosion.
Existing vessels can be retrofitted for H2SO4 storage. Indeed the appropriate coating must be applied, which indeed depends on temperature, concentration and on pressure. More information on corrosion with simultaneous diffusion of water and sulfuric acid, the following source may be handy: open source plastic info