To express the sentiment of being right in my conlangs, a number of slightly different constructions are used. However, first a quick overview of being right in the languages I speak and a few more.
In Finnish, the usual way would be olla oikeassa, essentially 'to be in (the) right'. In Swedish, however, the expression is ha rätt, 'to have right'. This also seems to be the way of expressing it in German, recht haben. Russian has прав, 'right, true' as a complement, so e.g. ты прав, "you (are) right/true". Onto languages I don't speak: The French and Italian expressions seem to be analogous - although 'to have reason' seem to be more literal translations. Spanish is a bit like Finnish, although with 'in truth' (en cierto) rather than 'right'. Bear in mind that I might be wrong on any of those beyond Finnish, Swedish, English and Russian. As a side note, for Finnish, English, German and Russian, there's a clear connection to right (the direction or side).
So, onto the conlangs!
In Bryatesle, being right is expressed using a verb that is closely related to the verb 'carry', verg, in the perfective aspect, with a quirky case subject, viz. the ablative.
In isolation, virga sometimes is used to express 'you're right'.
In Ćwarmin, being right is expressed by the demonstrative adverb olba/elbə ('this') in an adverbial form, olbaru, elbəri (essentially 'like this, like so, thus') or in the nominative definite olbutu, elbiti. The construction with olbaru/elbəri uses the reflexive possessive accusative:
~you have thus
you are right
The olbutu/elbiti form comes with the dative of whomever is right:
(s)he.dat right.nom.def(s)he is right
Unlike Bryatesle, Dairwueh uses the verb əduin, 'hold', but like Bryatesle, it uses a quirky case subject: the genitive. The verb is in the 3rd person II.
vedin ŋe ədu-ar
I.gen was.3sg hold-past.prtcpl
"my was held"
I was right
Ŋʒädär has a reflexive, locative expression.
(sint) prä-ŋä-bürs-äz ŋul-ər
(they) right-at-3pl/3pl-direct self-plur
they are right
Prän does in fact have a slight typological similarity to 'right', although it signifies a different type of direction: in fact, it signifies the east. prä-ŋä thus also signifies "in the east", but the only situation in which this appears with transitive marking is when signifying 'being right'. For those who haven't read how the reflexive works in Ŋʒädär, here's a post.
Sargaĺk uses a reduplication-like construction:
(ne-tta) tvadas tvadas yəra-si
I-peg truth truth put-1sg
I put truth (to) truth
I am right
Clearly, the pegative of the subject suggests that the two instances of "truth" are considered different constituents, however - one being a direct object and one an indirect object. Hence the (to) in the word-for-word English translation. Here, as well, the subject pronoun can be omitted.