Let’s say there is a small island nation that does not currently have an embassy in the United States. In exchange for letting a citizen of their country live at my house for free under the title of ambassador, and having them grant me dual citizenship, could I have my property declared an embassy where I would have diplomatic immunity?
The United States and Islandland will have to agree to exchange ambassadors. Even if the US agreed to the arrangement you propose, you wouldn’t have any kind of diplomatic immunity either as the owner of Islandland’s embassy property or as someone who resides in it. Only the diplomatic staff enjoy any kind of immunity.
If Islandland accredited you as its ambassador, and the US accepted that, then you would have diplomatic immunity in the US. I don’t know, however, whether the US will accept the accreditation of its own citizens as foreign ambassadors to the US.
The State Department has procedures to negotiate with local authorities to designate grounds as a mission. Localities can sometimes drive a hard bargain, because they lose property taxes and missions aren’t always the best neighors. For example, small countries sometimes don’t devote necessary funds to upkeep of missions, and some buildings here in DC get dilapidated and can be havens for rats and trash. Sad, but true.
As a US citizen, you could become on honorary consul from another country, no problem. It entails only ceremonial duties, but it is a cool thing to put on a resume. If you wanted to be an ambassador, as has been said, the US would have to accept you in that position. Countries don’t get to force diplomatic staff onto another country.