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.
Some adhesive systems like polyurethanes and silicones are inherently flexible, whereas others such as acrylics and epoxies can be flexibilized to provide shock-proof assemblies. There are also urethane-epoxy hybrid systems.
Epoxies are now used to provide crash-proof bonds in automotive body assembly operations, allowing very strong bonds to steel or aluminum structures. I recently used one of these adhesives to provide bonds on brackets that can add resistance to earthquakes in lowering the risk of damage to diesel and water storage tanks in a large manufacturing facility.