?250 is probably about the best price you'll get for a C-14 date, but there is a fund for community archaeology C-14 dates (https://www.cardfund.org/). Do be aware that it's not as straightforward as having something that contains carbon, sample collection needs to be done carefully to avoid contamination and if it's a timber sample, depending on the species and where in tree the timber came from, the date could be several hundred years out...