What does "tenable" mean to Shakespeare?
According to A Shakespeare Glossary by C. T. Onions, revised by Robert D. Eagleson (Oxford University Press, 1986), "tenable" means
Capable of being held, that may be kept back or held secret
The adjective has the same stem as the French verb "tenir" (and the Spanish verb "tener"), which can mean both "to hold" and "to keep". Hamlet is asking Horatio to keep the apparition of the old king's ghost secret (or "to himself") forever ("still").