When choosing a ceiling in an Irish pub, you should consider materials that are both functional and aesthetically pleasing, while also fitting in with the overall theme and aesthetic of the pub. Some popular ceiling options for an Irish pub include:

Exposed beams: Exposed wooden beams can add a rustic, traditional feel to the pub, and can also be used to create a cosy and inviting atmosphere.

Tin Ceiling: Tin ceiling tiles are a classic ceiling option that can add a vintage look to the pub, and can be painted or patina to match the style you want.

Coffered Ceiling: Coffered ceilings can add a touch of elegance to the pub, and can be painted or stained to match the style you want.

Wood Planks: Wood planks can add a rustic and warm feel to the pub, and can be painted or stained to match the style you want. 

Ultimately, the best ceiling option for your Irish pub will depend on your personal preferences, the layout and design of the space, and your budget. It's also important to consider the lighting options, as the ceiling will reflect the light and can enhance or detract from the ambiance of the pub.