Is the failure to give oneself hope of procreation, and the feeling of contentment when certain that it will not happen, considered despair of God's mercy?

We ask Allah to bless the questioner with righteous offspring. We advise her to strive with the means while her heart remains attached to Allah, Glory be to Him. She should not despair of His mercy; rather, she should have a good opinion of Him and entrust the matter to Him. For Allah blessed Ibrahim with a child in his old age.

If she turns to Allah and relies on Him, He will not disappoint her. He will either answer her prayer, or store it for her in the Hereafter, or avert some harm from her. So, she should not despair of taking the means, nor lose hope in Allah's bounty, and be certain that Allah will not disappoint her if the conditions for supplication are met.