If you have it handy, liquid silicone would do well, and then tape over the silicone. It's the stuff they use to deal fish tanks. Tape could get really leaky, it never worked for me.
Something else I've done is just getting a small glass jar and squeeze all the paint into it and get a sticker to label its color and whatnot.
The jar is the cheapest and more reliable option.
Definitely duct tape. Because, unlike the rest of the responses, (so far) it's the only one that will remain flexible as you use the paint and the tube slowly collapses. The trick will be to carefully apply the tape so that it adheres to all the ripples, nooks, and crannies. If you just slap it on there, it's not going to do much better than to redirect the flow from the hole
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Sure, that should work.
Seal it with Gorilla Glue.
I feel like tape would leak. Maybe hot glue?
Chewing gum will plug that
Bubble gum!
Duct tape probably
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