You have just a few options here.
Number one is silicone adhesive. This is one you must be careful with though. For general ornament repair or affixing rocks, wood and ornaments securely in the tank any clear 100% silicone is fine. Do not use any that are colored or contain antimicrobials and anti fungals. For actual aquarium repair only aquarium rated silicone is suitable. The difference between regular silicone adhesives and aquarium rated is tensile strength and adhesion properties. Aquarium rated is the only type strong enough to hold up to water pressure AND adhere to glass. It is not suitable for acrylic aquarium repair. Allow a minimum of one week cure time AFTER the cure time listed on the label before submerging it. The good news is this product is easy to find at any do it yourself store.
Number two is aquaculture rated epoxy. These two part epoxies are expensive and sometimes hard to get. It also requires careful mixing to work properly.They are specially formulated to be stable underwater and do not leach harmful chemicals as they age. Unless it clearly states "aquaculture safe' on the label, it is not suitable. You must also allow a minimum one week cure time before submerging it.
Number three is a urethane glue, such as the brand name Gorilla Glue. This polymer glue is 100% waterproof and has a cure time of only a day before submerged use. The down side to this glue is that it expands as it cures, so clamping of the parts is required. It may also "foam" out between the pieces, requiring a bit of carving and sanding.
