You don't say whether you've simply been renting or whether you're doing a lease-option.
If it's a lease-option, check the option document and see what it says about determining value. Often, the price is set up front. Then, when you apply for a loan, you pay (just as you would with any mortgage application) for the appraisal. If the price isn't set up front--if it says something like the sales price will be determined by an appraisal--the option should specify who pays for the appraisal.
If it doesn't, then you can either pay for one and decide whether to exercise your option, or simply walk away.
Or: Negotiate an extension to the option.
If it's a rental--no option attached--you need some way of determining the house's value. Again, though, the appraisal would usually be done after you've applied for a mortgage.
What you really need at this point is a CMA performed by a Realtor--a determination of the value based on recent comps. (Excluding the possibility that your option calls specifically for an appraisal, in which case that's what you'd need.)
You say the house isn't worth the amount the owners want. Well, then, don't buy it.
Or: Negotiate a lower price. Say they want $300,000. It's only worth $275,000. You say: "I'd like to buy the house, but I am not going to overpay. I'm willing to pay you $275,000, and that's it." Or: "I'd like to buy the house, but I am not going to overpay. I'm willing to pay you $250,000." Then you can negotiate up to around $275,000.
Seems to me you're in the driver's seat. You can buy the house, but not if it's overpriced. If you have solid evidence (a recent CMA) that the house isn't worth what the owners are asking, then present that evidence to them. Follow my suggestions above. There's no point in overpaying for a property. And there's almost no justification (except as noted above) for paying for an appraisal prior to the mortgage process.
Hope that helps.