I think that radiocarbon is the most effective method and I do not see any sound alternative to it.
Some animal remains could be dated through amino-acid racemization - but the reliability of this technique is debated - while tree remains with a good number of rings can be dated by means of dendrochronology.
As far as I know, I do not recall any technique more reliable and cheaper than radiocarbon.
Dendrochronology can offer more accurate results, but of course you are limited to only being able to use wood and you require a large enough sampling of wood items to make use of the method.
Radiocarbon is probably the most cost effective. See if others are also interested in getting dates from the samples/period - you may be able to split the costs.
Also bear in mind the precision of radiocarbon dating is not always great depending on the period. What kind of samples is it you are looking at?