In the case of a gift or sale of a property from parents to children, no real estate transfer tax is incurred. Depending on whether your boyfriend wants/should/must be included in the land register, they could save these costs completely or at least partially, and the equity would then be sufficient for the notary.
I don't think you will get financing for the 250,000 euros because it is not clear to me what you intend to do with the 20,000 euro gap. New kitchen? New furniture? Vacation?
Cost breakdown:
[*]House costs: 170,000€
[*]Renovation/modernization costs: 60,000
[*]Total costs: 230,000 => 20,000 euro gap
[*]Financing amount: 250,000
One person alone will not get the financing, but together I see few problems (however, then partial real estate transfer tax will apply again). Depending on the institution and exact conditions, you can get 230,000 euros for something between 600 and 800 euros per month. That should not be a problem. Depending on how well the house is insulated, your costs will be around your current warm rent or slightly higher.
How urgent is the sale from your parents' side? Do they need the money immediately, or can they still wait with the sale? If they can still wait, use the time and try to increase your current monthly savings rate of 1,200 euros and create a reasonable equity cushion.
I have one more question: in which federal state do you live?