Tag Questions – Using ‘They’ in Tag Questions with Everybody/Nobody

A sentence that begins with There is is called an existential clause, the sentence refers to the existence or presence of something.

In English, existential clauses usually use the dummy subject construction (also known as expletive) with there, as in "There are boys in the yard"…

In the OP's sentence, the subject is not "nobody" but there (is). Consequently, the rule dictates that you should repeat the same subject used in the clause to make a question tag.

There is nobody in the garden, is there?

As illustrated by FumbleFinger's comment, when the main clause begins with the subject "nobody", or "everybody", "everyone", "no one", etc. THEY, also called the singular they, is used in the question tag.

Nobody is in the garden, are they?

The pronoun nobody makes the clause negative, so the verb used in question tag should be positive. However, if the pronoun everybody/everyone is used, the question tag should be in the negative.

Everybody is in the garden, aren't they?

Wikipedia explains that the singular they is used with the following pronouns: someone, anybody, everybody, everyone, nobody and no one. Even though these pronouns are singular, native speakers prefer to use the genderless "they" in question tags while Wikipedia argues these pronouns:

have an "implied plurality" that is somewhat similar to the implied plurality of collective or group nouns such as crowd or team, and in some sentences where the antecedent is one of these "implied plural" pronouns, the word they cannot be replaced by generic he, suggesting a "notional plural" […].

and provides the following examples

• “Everybody was crouched behind the furniture to surprise me, and they tried to. But I already knew they were there.”
• “Nobody was late, were they?”