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In that context 'parking' functions as an adjective, so it doesn't take -s, it's not plural. Below, the nouns 'space' and 'spaces' agrees in number with the verb:
Ex: There is a space.
Ex: There are spaces.
Ex: There is a parking space.
Ex: There are parking spaces.
Ex: There is parking space. <means, there is room, an area>
All of the above are correct.
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