Contrary to what everyone else has said, there is a way to suspend GC, though it's very convoluted.
If you call a native function via JNI, in between the native code calling GetPrimitiveArrayCritical and ReleasePrimitiveArrayCritical, GC is suspended. It has to do this because it is the mechanism used for sharing memory between Java and native code, and GC may move objects around in memory.
So to utilise this you'd need to create a JNI function which calls the former, then polls a flag written to that critical array (which could just be a byte[1]) waiting till it sees the flag before calling the latter. When the Java code wishes to suspend GC it would call the JNI method and when it wishes to resume GC, set the aforementioned flag (I believe reads/writes to the critical array are volatile, so the native code would see the flag immediately).
Now I'm not saying this is a good idea, and certainly not the correct solution to the OP's problem. But if you absolutely had to temporarily suspend GC for some reason (perhaps you wish to manipulate raw memory via sun.misc.Unsafe and needed to ensure objects were not moved about by GC whilst doing so), that's how you could achieve it.