It depends where you are. In many tropical areas low soil pH can compensate for high manure pH. In the temperate zone, forest soil under pine trees is often acidic with pH of 5 or less. Mixing with acidic soil might thus be the cheapest option especially if you produce large quantities of compost.
Elemental sulfur reacts slowly with the soil and well react faster during the biological activity of anaerobic composting. It should be applied and worked into the soil to a depth of 6 inches. I agree with Upendra recommendation because the feasibility and availability of sulfur is well known
Iron sulfate is a fast acting soil-acidifying amendment. Changes in pH level usually occur with 3 to 4 weeks.
Organic compounds such as sphagnum peat moss, compost, and manure can be used to lower soil pH. Lactic acid from dairy waste-water could be used to enhance the biological activity in the alkaline compost and reduces the pH.