[Tearvan]

Libertas Omnium Maximus had a brief (and relatively unsuccessful) attempt to establish a colonial empire between 1880 and 1910 (approx.), but this would probably push the timeframe forward too much, seeing as you had hoped for an 1800s independence. Libertas Omnium Maximus wasn't actually founded until 1802, so you might have better luck with Valahandia, a puppet of mine that had an extensive colonial presence between roughly 1500(ish) and 1700. Most of its colonies achieved independence in the late 1700s and early 1800s. Though its culture has never really been all that developed, it was a Celtic-inspired empire that gradually began to integrate Christian naming conventions and customs as the years went on.

Valahandia actually sounds pretty interesting to be my nation's colonizers, the history of Valahandia matches pretty well with what I have in mind.