In English, we prefer to negate the verb think rather than to use a negative in the content clause which represents the actual thought involved. This is also true with verbs like want and believe. So we prefer:
to
And we prefer:
to
I think that the problem with the sentence:
- I think there couldn't be any trains running today due to the strike
doesn't really have anything to do with the verb could - although it is tempting, and indeed not unreasonable to think so. The real problem is that we would far rather negate the verb think than the verb phrase in the subordinate clause - which in this instance is headed by the auxiliary verb could:
- I don't think there could be any trains running today because of the strike.
The sentence above seems fine in spite of the verb could.
If you're interested in subordinate negation implication, you can read more about it here
Hope this is helpful!