Corporate pilot reported receiving a low altitude alert from ATC when the aircraft descended too quickly on final approach. Flight crew returned to correct altitude and continued.

Narrative

We were being vectored for a RNAV approach when ATC offered us a visual approach with the runway in sight. We were cleared to descend to 3000 feet and direct to ZZZZZ; a waypoint on the approach. The Pilot Flying then accepted the visual approach. We were at 8000 feet at 250 knots. The Pilot Flying was attempting to descend and slow down and was having trouble getting good speed control. We were able to get flaps to 20 and the speed under control. The pilot then asked for the FAF altitude; 2200 feet; to be selected. As were turning to intercept the runway center line; we descended too quickly and Tower notified us of a low altitude alert. The pilot immediately leveled off and we passed the FAF at the required altitude. I hesitated to dial in 2200 feet in the altitude selector too far from the FAF and with a higher than normal descent rate. I should have waited until the aircraft was on path before allowing the aircraft to descent too quickly thru 3000 feet. We were in VMC conditions and had the airport in sight at all times. After the passengers disembarked; we discussed how we could have better flown the visual approach. Speed control; best drag configuration; situational awareness; and better CRM procedures were all covered.