Whether it's an epic quest to defeat evil or a trip to the grocery store, any and every story can have conflict. Even happy stories. "Feel Good" stories usually make you feel good because it involves someone overcoming some adversity. .
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Don't think about conflict as fist fights or someone acting directly against someone else. Sometimes, it is just that and it is plain to see. However, many times it can be much more subtle. Someone could be stuck between two options, both of which are good for them. Someone might have a seemingly great life but still struggle with something about themselves. Not every story needs a hand-wringing n'e'rdowell lying in wait to ruin everything. .
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Internal or external, conflict moves your story forward. Even if your setting never changes, if you only focus on one person doing one thing, the conflict is what keeps us engaged. You don't always have to stick to intro, riding action, climax, falling action, although it is a tried and true method.
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The trouble with this is that many writers get hung up on whether or not their conflict is interesting enough. Listen carefully. If you put your heart into it, readers can be captivated by a quiet dinner alone. Did they choose to be alone? If not, what happened? If so, why? Are they stressed about work or family? If they're pleased as punch, what's got them in such a great mood? Conflict can be told in the past, as it's happening or even as it might come to pass.
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While saving the world is a heavy burden and almost always entertaining, don't feel pressured to constantly raise stakes. Sometimes low stakes make for better reading if it gives us more time to know the characters. Likewise, what may seem like low stakes could feel like the end of the world.