Trump said Comey told him once at dinner and twice via phone that he wasn't under investigation... (By the way, if someone asks for assurance 3 times that they aren't under investigation, isn't that a good reason to think they SHOULD be under investigation?)

Assuming he didn't bug the FBI director at dinner, when could he have done it legally?
It turns out it would be legal in Washington DC for him to record the phone conversation:
http://www.dmlp.org/legal-guide/district-columbia-recording-law

The District of Columbia's wiretapping law is a "one-party consent" law. DC makes it a crime to record a phone call or conversation unless one party to the conversation consents. See D.C. Code § 23-542. Thus, if you operate in DC, you may record a conversation or phone call if you are a party to the conversation or you get permission from one party to the conversation in advance. That said, if you intend to record conversations involving people located in more than one state, you should play it safe and get the consent of all parties.

However in Florida it isn't, and we all know how much time Trump spends there 'working':
http://www.dmlp.org/legal-guide/florida-recording-law

Florida's wiretapping law is a "two-party consent" law. Florida makes it a crime to intercept or record a "wire, oral, or electronic communication" in Florida, unless all parties to the communication consent. See Fla. Stat. ch. 934.03. Florida law makes an exception for in-person communications when the parties do not have a reasonable expectation of privacy in the conversation, such as when they are engaged in conversation in a public place where they might reasonably be overheard. If you are operating in Florida, you may record these kinds of in-person conversations without breaking the law. However, you should always get the consent of all parties before recording any telephone conversation and any in-person that common sense tells you is private.

In addition to subjecting you to criminal prosecution, violating the Florida wiretapping law can expose you to a civil lawsuit for damages by an injured party.

Federal law is 'One party consent' just like DC

That said, I don't think Comey ever gave Trump those assurances, or that Trump recorded him.