This blog has been getting a number of hits over the last few days from Google search terms such as "can you have a funeral on purim", mainly due to this post.
I don't know why I didn't think of this earlier, and it's too late for this to be of any help this year, but people were probably doing those searches for a reason. :( I'll answer the question now (since this post isn't so helpful in determining contemporary practice), in case someone ends up at this blog next year for the same reason.
First of all, if you got to this post through a search about funerals on Purim, I offer sincere condolences on your loss.
Second of all, the answer is yes. There can be funerals on Purim.
I had the misfortune of attending one when I lived in Israel. (The funeral was on 14 Adar, outside Jerusalem.) Traditionally, eulogies are not delivered on Purim and other joyous holidays. However, in practice, this can be waived with "Today is Purim; this is not a eulogy" boilerplate at the beginning.