Chairs can be at tables, under tables or on tables. Unless they're levitating they can't be over tables.
On is handled with the -Daq suffix: raSDaq 'oHtaH quS'e' The chair is on the table.
Although notice that it includes some ambiguity: this could also mean The chair is at the table. If you absolutely had to make the distinction, you could say raS yorDaq 'oHtaH quS'e' The table is on the top surface of the table and raS Daq 'oHtaH quS Daq'e' The chair's location is the table's location. (Daq is a separate Klingon word meaning location.)
Follow-up question then: Does DeSwarDaq mean in the cupboard or on top of the cupboard or both?
It can mean either, depending on context. -Daq signals that the noun it's attached to is the location at which the verb happens or the location the action of the verb is heading toward. It is not more specific than that.