I use this serial # database for Colts. Find your gun on left margin, select it, and you get serial numbers by year. Click on this link:
The number you see, for a given year, is the serial number that was manufactured at the beginning of that year. You bracket your serial number within two consecutive years. So, in your case, S/N 88,789 lies between 1858 (85,000) and 1859 (90,000). Your gun was made late in 1858 (likely late August - early September assuming fairly even monthly production rates, a fairly reasonable assumption before the war began). During the war, rates of production changed significantly within some years as contracts were obtained and production capacity was increased to deliver on those contracts.