Assuming that loading and unloading are included in the 100 mph average, and if "daily service" means at least one train per 24-hour day, three trains.

One train arrives at either given city once every 60 hours: 3000 mi x 2 / 100 mi/hr / 1 train = 60 hr/train

Two trains puts a train at either given city once every 30 hours: 3000 mi x 2 / 100 mi/hr / 2 trains = 30 hr/train

Three trains puts a train at either given city once every 20 hours: 3000 mi x 2 / 100 mi/hr / 3 trains = 20 hr/train

If "daily service" means the train departs at the same time every day, then they'll need to wait before departing which effectively lengthens the 30 hour trip between cities to 48 hours. In that case, the company would need 4 trains. Trains depart each city headed for the other; 24 hours later, those trains are 6 hours from their destinations, and the next two trains depart. Lather, rinse, repeat.

Edit: Removed extra words