Fractional jet First Officer reported receiving a GPWS terrain alert on a visual approach to TUPJ/EIS airport.

Narrative

While arriving at TUPJ we received a terrain alert while performing the visual approach to rwy 7. During the arrival inbound I briefed the 2 appropriate procedures and what the approach would look like and the rising terrain that is off to the north that we would encounter in alignment with the final approach segment of the visual. We successfully flew the RNAV GNSS-A (Global Navigation Satellite System) and had a complete visual path with runway 07. We had been cleared to land and the Captain loaded the visual to give us a glide path appropriate with runway 7 and showed us about half dot high on the path. I made the corrections to get lower and when in the process we got the terrain alert. I leveled the descent and pitched up slightly to correct the actions. The alert went away and I continued the visual. While on a very short final fully configured to land we got a false alert again for terrain and didn't have any terrain associated with the alert and we landed safely.Suggestions: In the future I will not continue the approach at this airport or any airport if I receive a terrain alert and will execute a missed approach and come in for another approach.