If you really want a pair of verbs, that might be s’asseoir and se lever. Se tenir debout is not incorrect but a little too "technical".

Otherwise, adjectives instead of verbs would probably better suit as an opposite pair: assis / debout.

Here is how some English sentences (From Lambie’s comment) can be translated to French:

Do the children stand or sit during the meeting?
Les enfants sont assis ou debout pendant la réunion ?

Where should I stand when you take my picture?
Où est-ce que je dois me mettre quand tu me prends en photo ?

We were standing in the hall when the president arrived.
On était debout dans le hall quand le président est arrivé.

We would likely drop debout in the last sentence unless that’s a detail that really needs to be expressed.

You have two basic meaning connected with the verb "to sit".

The first is that of a STANCE verb, that is a verb that confers no idea of ACTION (DYNAMIC verb) and no idea as that conferred by a STATIVE verb;

(CoGEL 4.32) Type C stance
In addition to the stative verbs noted above, there is a small but important
class of verbs which express the situation type we will call STANCE, and which
are intermediate between the stative and dynamic categories. The main
stance verbs are live, stand, sit and lie, and they are characterized by their
ability to be used both (a) with the nonprogressive to express a permanent
state, and (b) with the progressive to express a temporary state:
♦ James lives in Copenhagen. [permanent residence]
♦ James is living in Copenhagen. [temporary residence]
♦ The city lies on the coast. [permanent position]
♦ People were lying on the beach. [temporary posture]
♦ His statue stands in the city square. [permanent position]
♦ He is standing over there. [temporary posture]

Similar possibilities exist with the perfective aspect: the perfective
progressive, as well as the simple perfective, can be used to refer to a state
leading up to the present:
♦ [1] I have sat here for over two hours.
♦ [2] I have been sitting here for over two hours.

Speakers differ, however, in judging how to choose between the constructions
of [l] and [2]. Some speakers feel that [2] suggests a more temporary state,
whereas others feel there is little to choose between the two variants. There
is also sometimes a feeling that [l] is different from [2] in implying that the
‘sitting’ is concluded at the present moment, while [2] implies that the posture
may well continue into the future.
Because of its intermediate status, the stance action type illustrates an
element of gradience (cf 2.60) in the stative dynamic contrast. At one end of
the stative/dynamic scale, as Fig 4.27 shows, there are acts which lack
appreciable duration, such as nod and arrive; at the other end, there are
permanent qualities such as be tall. To some extent, the stative/dynamic
dichotomy is an artificial division of this continuum.

With respect to that meaning the English verb is "to sit"; its translation in French is the verb "asseoir" in the passive form ("être assis") or verbal expressions such as "rester assis", .

• He is sitting on this chair all day long.
  (Il est assis sur cette chaise toute la journée.)

• He does nothing but sit all day long.
  (Il ne fait rien d’autre de la journée que rester assis.)

"To stand" is in the same category, and is translated into French by"être debout".

• He is standing in the hall.
  (Il est debout dans le couloir.)

The second meaning is that of an action verb. The form of the English verb is again "sit"; however, it is used differently: it is used in combination with the particle "down" to form the phrasal verb "to sit down". The translation of that verb in French is again based on the same form, "asseoir"; however this time it is the pronominal variant that is used: "s’asseoir".

• I sit down when I am tired.
  (Je m’asseois quand je suis fatigué.)

• There is nothing to sit on.
  (Il n’y a rien pour s’asseoir.)