Short answer. No. The Civil Code lets a creditor demand a replacement guarantor if the original one becomes insolvent, but that rule does not apply when the creditor specifically required and stipulated that a particular person be the guarantor. In that case, the debtor cannot substitute anyone else, even if the named guarantor becomes insolvent.
What the law says
The case is excepted where the creditor has required and stipulated that a specified person should be the guarantor
Civil Code, Article 2057 — Replacement of a Guarantor. Read the full provision →
What the law says
If the guarantor should be convicted in first instance of a crime involving dishonesty or should become insolvent, the creditor may demand another who has all the qualifications required in the preceding article
Civil Code, Article 2057 — Replacement of a Guarantor. Read the full provision →
The general rule, and your exception to it
As a general rule, if a guarantor is convicted in first instance of a crime involving dishonesty, or becomes insolvent, the creditor may demand another guarantor who has all the qualifications the law requires. That rule exists to protect the creditor, letting them insist on a replacement when the original guarantor stops being a reliable safety net. But the Civil Code carves out an exception exactly for your situation: the case is excepted where the creditor has required and stipulated that a specified person should be the guarantor. Since the whole point of the rule is protecting the creditor's interest, the creditor can also choose to give up that protection by naming one specific person and no one else.
Why the debtor cannot force a substitution
When you specifically insisted on one particular guarantor as a condition of the deal, that insistence became part of the agreement itself, not a default that either side can walk away from later. The debtor's ability to offer a substitute guarantor exists to serve the creditor's need for security, and here you already told the debtor whose security you wanted. Insolvency of that specific guarantor does not revive a right to substitute someone else, because the parties bargained around the general rule from the start. The debtor is bound by what was agreed, not by what becomes convenient once the chosen guarantor's finances change.
What you likely still have to live with
The practical consequence is that if your named guarantor becomes insolvent, you may be left without effective security for that particular guaranty, since the debtor is not obligated to supply a replacement. This is the trade-off for insisting on a specific person rather than leaving the choice open to whoever meets the general qualifications. If you want protection against this scenario going forward, that protection needs to be built into the agreement itself, rather than assumed from the general rule on replacing a guarantor who becomes insolvent.