You have a wide range of possibilities here. Normally, you would require an adhesive that has been toughened with a rubber for this. However, there are examples where very rigid, quite brittle adhesives are successful in countering vibration.
The most well-known application is the use of so called “anaerobic” adhesives for threadlocking (i.e., the vibration proofing of threaded assemblies). Despite the brittle nature of these threadlockers, they effectively adhere, fill the space between threads, and prevent loosening of assemblies during vibration.