Don't say it:
Timbo and I's anniversary was so amazing!
Don't ruin your anniversary like this. Timbo will still love you, but he'll be embarrassed.
To fix it, you can say:
Timbo and my anniversary was so amazing!
What? Not Timbo's and my anniversary was so amazing!? No, because you and Timbo share the anniversary, so you only use one possessive (my). (If you're talking about unshared possessions, it goes like this: Timbo's and my Corgis got in an amazing fight again!)
But you're right, the fix sounds weird. So why not redirect the whole thing into something like,
Our anniversary was so amazing! or, Timbo and I had an amazing anniversary! ?
Right again, because every time an American says something is amazing the Daughters of the Air have another day added to their amortization. Let's try once more:
Our anniversary was so [any adjective but amazing]!
There you go.
If that still isn't sitting well with you, you can always try one of these:
Hot enough for ya!
How bout them Hawks!
Are you still nursing that baby!