Ask yourself WHY you want your teams to lighten up. It's important to think about this, because it will help you clarify existing team collaboration/communications problems and how this may affect your team: beyond the fact that yes, it is nicer when people are friendly and share a joke or two, how does the current situation actually affect your project? Are people not sharing information, not collaborating efficiently, don't feel free to speak and raise issues, are at risk of leaving the project, etc.?
Talk to your team about it. Once you can articulate reasons for changing the way things are (eg. "if we build collaborative, friendly, positive relationships, we will be able to go through difficult times in a more effective way"), address it directly with you team. Do it in an informal way, one-on-one. Ask them how they feel about the way things are going, what would they like to do differently when it comes to team collaboration and why.
Create opportunities to introduce collegiality. It could be making things more personable like having a directory of people with photos and a little about themselves, using social media to help people connect quickly and in a more informal way, congratulating people for resolving a problem or completing a task together, celebrating project successes, wishing happy birthdays or personal congratulations, showing a funny or inspiring video (TED is a good source) or sharing an anecdote as an introduction to a topic, etc.
Be funny and respectful. Humour can be difficult across borders, and even between different personalities. Something funny to someone may be disrespectful to another. Work out who will share a joke and who won't and when using humour, stay clear of the un-politically correct stuff.