Dcn. Jeff has it right.
The dalmatic is the proper outer garment for the deacon during Mass. This is addressed in the General Instructions for the Roman Missal, which states:
- In the sacristy, according to the various forms of celebration, there should be prepared the sacred vestments (cf. nos. 337-341) for the Priest, the Deacon, and other ministers:
b) for the Deacon: the alb, the stole, and the dalmatic; the latter may be omitted, however, either out of necessity or on account of a lesser degree of solemnity;
First, we should note that the stole is always used with the dalmatic.
“Necessity” is easy. That means if the parish can’t afford dalmatics, they can be omitted.
“Lesser degree of solemnity” is a bit vague. I would interpret this as meaning daily Mass. All Sunday Masses are meant to be solemn (hence their holding the rank of “solemnity” on the Church calendar). This decision ultimately lies with the bishop, or the pastor.
I go to two parishes: At one, the parish only has a white dalmatic, which is used when possible. The rest of the time, the deacon wears only a stole.
At the other, the pastor has specifically instructed that dalmatics must be used during Mass. The parochial vicars, visiting priests, and the deacons are not allowed to omit them.
Again, Dcn. Jeff mentioned that a cope may be used when the deacon presides at extra-Missam liturgies (Vespers, Baptisms and Marriages out of Mass, et c.). In this situation, the deacon may use an alb and stole, or a cassock and surplice.
However, if the deacon is assisting at an extra-Missam liturgy, the dalmatic is appropriate, while the priest who is presiding wears a cope.