You can certainly take antidepressants while on Suboxone, but you'll have to work with your doctor very closely.
Suboxone (buprenorphine/naloxone) is a treatment for opioid use disorder (OUD). Sometimes, this medication isn't quite enough to help you overcome all of your addiction triggers. If you have depression, you may need antidepressant medications too.
In studies of people with addictions, 93% of people also had depressive symptoms.  Depression can lead to a relapse to drugs, even while you're taking Suboxone. Using medication to simultaneously treat depression could help both the depression and the risk of relapse to OUD. Compared to people getting no antidepressants, those who did stayed in treatment for OUD longer.
Some antidepressants can interact with your Suboxone. You should always talk to your doctor while using both of these classes of medications together. You should report any problems you experience right away.
There is no “right” antidepressant to take with Suboxone. The medication that is best is the one that works best for you. There are multiple classes of medications used to treat depression. Some of them are very safe to use with Suboxone while others may have some additional risks, particularly any that are also sedating.
These are a few categories of antidepressants that are commonly used:
Selective serotonin reuptake inhibitors (SSRIs) are first-line medications that are commonly prescribed to treat depression. They're considered safe, effective, and tolerable when compared to other antidepressants.
Plenty of medications fit into the SSRI classification. Common names include Prozac, Fluoxetine, Sertraline, Citalopram, Escitalopram, among others.
Tricyclic antidepressant medications help increase levels of serotonin and norepinephrine, which leads to a buildup and improved depression in some people. Examples include Nortriptyline and Amitriptyline. While many people do take these medications with Suboxone, combining antidepressants like this with buprenorphine-based medications can lead to increased sedation and drowsiness. If you notice this issue, talk to your doctor.
Monoamine oxidase inhibitors (MAOIs) were the first antidepressants available. Some doctors still use them, but they're not as commonly used anymore. They may also cause some sedation and drowsiness, and so using them with Suboxone is not contr-indicated, but may not be ideal. 
Serotonin and norepinephrine reuptake inhibitors (SNRIs) are another safe and common antidepressant medication class. Examples include Venlafaxine (Effexor) and Duloxetine (Cymbalta). In general, SNRIs are not sedating and are safe to take with Suboxone.
All the antidepressant medications we mentioned here, along with Suboxone, require a prescription. You can't take these drugs without talking to your doctor first.
But using these two types of drugs at once can require some monitoring, so you can stay safe and avoid being overly sedated.
Some people experience an improved mood and less depression due to buprenorphine medication alone. And some people only need antidepressant medications for a short time, and they continue to use Suboxone indefinitely.
Everyone is different. Talk with your doctor about how you're feeling now, how you feel on antidepressants, and what should come next. Together, you can craft the right plan to treat both an opioid use disorder and a depressive disorder simultaneously, and safely.