If I understand your question, you want to assemble two sequences at a time, one forward strand, and the other reverse strand, the two sequences meet in the middle. Pretty much any overlap-based assembler can do the trick. However, since there are only two sequences, you need to decide how to call consensus bases when the overlapping region of the two sequences disagree.

Important parameters are max allowed hangs, identity cutoff, and minimum overlap length. Be aware that these parameters affect the outcome, even though you are likely going to use the defaults.

                    overlap  hang
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>                     Forward                      
                    |||||||
                    <<<<<<<<<<<<<<<<<<<<<<<<<<<<< Reverse

For command-line programs, use EMBOSS merger or CAP3. I am not familiar with many GUI options, but have used Sequencher in the past to assemble small number of reads.

If there are substantial number of bad bases of N's towards the end of each sequence (which will prevent two sequences from merging), consider trimming based on quality.