What are some give-type verbs that cannot undergo straight dative alternation?

The following dative alternations sound off to me:

I want to donate my clothes to charity. --> I want to donate charity my clothes.

He has to submit his paper to his teacher. --> He has to submit his teacher his paper.

If these words cannot undergo dative alternation, is there a rule explaining why?

Also, if members of this community would like to contribute to the list of give-type words that cannot undergo dative alternation either in the comments or answers, that would be greatly appreciated.

You are right; they are 'off', in fact they're ungrammatical.

"Donate" and "submit" are mono-transitive verbs; they can only take direct objects. With these verbs, the recipients or beneficiaries of the objects have to be expressed by PPs headed by "to", as your left-hand examples correctly show. But, crucially, they're not indirect objects; the objects of “to" ("charity" and "his teacher") are called 'obliques' because they're related to the verb only indirectly, via the preposition.

That explains the ungrammaticality of your right-hand examples: with certain verbs, you cannot express the recipient of the direct object with a noun phrase indirect object, but only in a PP.

Other verbs belonging to the same category (i.e. requiring "to" for the recipient) are "announce", "confess", "contribute", "convey", "declare", "deliver", "exhibit", "explain", "mention", "narrate", "refer", "return", "reveal", "say" and "transfer".