Formal/Neutral:
* J'essaie de sourire. (Most direct translation)
* Je fais de mon mieux pour sourire. (I am doing my best to smile)
Informal/More expressive:
* J'essaye d'arborer un sourire. (I am trying to put on a smile)
* J'essaye de faire un sourire. (I am trying to make a smile)
If you want to emphasize the difficulty of smiling:
* J'ai du mal à sourire. (I have difficulty smiling)
* Je me force à sourire. (I am forcing myself to smile)
The best choice will depend on the context of your sentence and the tone you want to convey.