Gosh they really are serious then
Do the cats have a vaccination history already? This may help to convince them.
The test they would be wise to ask for is the Feline Leukemia Virus tests (FeLV).
They may also be averse to taking FIV+ cats too.
There is much fear surrounding both these viruses, and you need to know what the differences are, and the reliability of the tests for each, as false positives and negatives are common. FIV is not the death sentence many people believe it to be and ignorance has lead to the unnecessary demise of thousands of beautiful, healthy cats. FeLV however is serious, highly contagious and potentially lethal.
As for them paying for the tests, ask your vet beforehand how much the cost will be. The couple could write a cheque made payable to the vet to cover the fee, perhaps. That way everyone is sticking to the agreement.
In any case, ask your vet for a copy of the results, if they choose not to take them, you will have these for the next potential owner.
The secondary tests take a few days to complete as they are sent to Glasgow for testing. In healthy cats with limited risk (i.e.indoor cats) this would usually only be required if a positive result is found (that may be a false positive). You will get the results of the primary (ELISA) tests back within 24 hours, as these are usually performed in the vets own premises.
Please check out the Catwork site here for more information. They have been looking after FIV and FeLV cats for years and know the realities of these diseases and the effect bad information out there has had.
http://www.v63.net/catsanctuary/felv.html