Powers are either explicitly stated or they are implied. Since nothing in the Constitution explicitly states who may suspend habeas corpus then you are implying it.
Article I, Section 1 states so explicitly for ALL of them.
Where?
But since congress cannot generally delegate its power, no. A state could not do that so long as it was still in the union.
Congress delegates its power all the time. So they can allow the states to do that if they simply pass legislation stating so?
That is a contrary assumption without basis or support (sort of like proving from a negative).
See? I knew it would be a hoot.
Your premise is once again false. Congress is explicitly stated in Article I, Section 1, which defines its own application to extend over the rest of the that article. Since the habeas corpus clause is indisputably within that article it is governed by Article I, Section 1.
Where?
"All legislative Powers herein granted shall be vested in a Congress of the United States"
Once again, exactly what do you not understand about this clause?
Congress delegates its power all the time.
They do, but they aren't supposed to and at times when they step over the line with more eggregious cessions of power they get struck down on a separation of powers ruling.