Deepak is an unpleasant person, but we all ____________ because his sister is a close friend of ours.

The phrases given in the options have the following meanings them:

1. put him down: the phrase simply means to put someone down
2. put him aside: it might imply ignoring, but it does not have an indirect meaning usually
3. put up with him: the phrase means to tolerate someone (or their actions, despite them being bad)
4. put along with him: although it might not have a meaning in particular, it can be close to the meaning of 'go along with'
   

In the given sentence, Deepak is described as an unpleasant person. It makes sense that people are tolerating him because they have a friend who is a close relative of his; therefore, option C is the correct answer.