As stated by @Personne in the comments, you can use the verb s’entendre.

Les deux frères s’entendent bien.

As stated in the comments, rapport can also mean intercourse in French, so it could be ambiguous to use this without adding more context. However, it is a correct usage (see the CNRTL definition, section III.E.), and it can work very well, for example:

Les deux frères travaillent ensemble et ont de bons rapports professionnels.

or

Malgré la séparation durant leur enfance, les deux frères sont restés en bon rapports.

However, to answer your question, I don’t think it makes sense to use rapport as a singular because it designates the (multiple) interactions two people can have with each other. If you wish to use a singular word, use relation, which defines the link itself between two people (it can actually also be used in its plural form but let’s not go too deep into details).