SPME is a pretty good method, but if you want an alternative and depending on your target analytes, dynamic headspace GCMS would be an option to explore.
For less volatile components solvent extraction might be one to look at:
Equilibrium headspace, purge and trap, solid phase extraction, or one of the variants of solvent extraction might work but to give useful answers we have to know what analytes you are looking for, what equipment you have, and what is wrong with SPME.
If you decide to work with SPME , you need tu make repetitions, to ensure reproducibility of the method. You need to select the best results that show fiber to your samples. Is key to make an experimental design.