A fall in interest rates results in a fall in the coupon rates of bonds that are issued after the fall in interest. The coupon rate of a bond is an amount that the issuer is willing to pay the buyers of the bond for lending their money. When the interest rates fall, the returns that investors can get from investing their money in risk-less assets decreases, this induces them to buy bonds even if the coupon rate is lower as it is still higher than the return from the other option.
The coupon yield of bonds that have been issued remains the same for the bond irrespective of the change is interest rates as they are fixed when the bonds are issued. The yield to maturity of a bond issued at par value also remains the same.