Latin translation for the Serenity Prayer?

Question

I'm looking for the latin translation of the Serenity Prayer:

God,
Grant me the serenity to accept the things I cannot change,
The courage to change the things I can,
And the wisdom to know the difference.

Here's what Wikipedia says:

Deus,
Dona mihi serenitatem accipere res quae non possum,
Fortitudinem mutare res quae possum,
Atque sapientiam differentiam cognoscere.

Is that correct?

A change I might make is to use "Domine" instead of "Deus", what do you think?

[Edit:] Sooo almost two years after posting this, it's finally been done on March 15!

A massive thank to TKR for the help on the translation!

Here are two pictures of during and just after :)

Answer 1

The Wiki translation is bad in several ways (the first line is missing the word "change"; the infinitives are not good Latin; the verbs in the relative clauses should be subjunctive; and the word choices are mostly unidiomatic translationese). Here's an attempt:

O deus / domine, dona mihi animi aequitatem, ut quae mutare non possim, clementer feram; ac fortitudinem, ut quae mutare possim, mutem; ac sapientiam, ut haec ab illis discernam.

I've replaced serenitas, which is mostly used as a description of weather, with a more idiomatic phrase animi aequitatem "serenity of mind". A little looser, but probably more natural Latin, would be aequum animum "a serene mind". For "accept" in the sense of "endure without struggling", the usual word is fero, often with some adverb such as clementer "gently". And for "know the difference" a more natural Latin expression is something like "tell the former from the latter", which is what haec ab illis discernam means.

To be freer yet, I think it sounds better with the order of the first two parts reversed, and the second of the two mutare "to change" elided:

O deus / domine, dona mihi fortitudinem, ut quae mutare possim, mutem; ac aequum animum, ut quae non possim, clementer feram; ac sapientiam, ut haec ab illis discernam.